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# Chem 1105 Lab Manual Answers

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When a double replacement reaction occurs, the cations and anions switch partners, resulting in the formation of two new ionic compounds AD and CB, one of which is in the solid state. A class glassware is more accurate. Pre-Lab Lecture Videos. 3\times10^3\ \mathrm{J/{^\circ C}}$It is important that heat capacities are positive, think about what it would mean if this were a negative value. University of Alabama, Huntsville General Chemistry I sample exams with answers, from Prof. Bush’s peers in engineering were certainly. MCV = 1105, MVC= 1095 If that way was accepted the best answer I can give you is 905. Understand the relationship between equilibrium constant and concentration. Urban Climates is the first full synthesis of modern scientific and applied research on urban climates. Corequisites: CHEM 1311. Teachers who have awaited the appear- ance of this t,hird and final xuthorized re- vision of CHEM Stndy shall be rewarded. Engaging Students Empowering Educators. 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Standard molecular biology techniques were used throughout this study (Sambrook and Russell, 2001). You need anywhere from 34 to 38 questions correct, depending upon the difficulty of the form of the CLAST you are administered, to "pass" this test. It explains why the study exists. Laboratory Activity: Teacher Notes. FREE CLICKERS. Rheumatoid arthritis (RA) is a chronic systemic inflammatory disease of unknown cause. Welcome to bluedoorlabs. Hydrogen sulfide, $$\ce{H2S}$$, is formed by the direct combination of an acid (source of $$\ce{H^{+}}$$) and. Final Exam Covers the experiments of the second half of the semester. If the sample volume is not enough, it can be diluted with normal saline. Biology Elective: Four hours from the following: BIO 3122, 33 22 , 3330, 41 00, 4107, 4108, 4307, 4308 , 4401 HISTORY/ SOCIAL SCIENCE. 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Basic earthquake science seeks to understand how earthquake complexity arises from the brittle response of the lithosphere to forces generated within the Earth’s interior. The Chemistry Department offers a Departmental Examination to award upper division credit for CHEM 3321 and CHEM 3322 (the current majors' organic chemistry lecture sequence) by successful performance on an examination covering the fundamental aspects of the two. One has to. See the complete profile on LinkedIn and discover Scott’s connections and jobs at similar companies. Palo Alto, CA: Mind Garden, Inc. You can follow the question or vote as helpful, but you cannot reply to this thread. Develop lesson plans. Mandy Cook Email use D2L online course resource ([email protected] Maharashtra State Board of Technical Education (MSBTE) is an autonomous Board of Government of Maharashtra mandated to regulate matters pertaining to Diploma Level Technical education in the state. 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Chem 1105: Redox Lab Kwantlen Polytechnic University Updated on May 26, 2011 Surrey Page 2 Precision Calculation: Choose three runs whose values are closer to each other, and find the % difference between runs (see page 31 of lab manual for the formula) Calculations: (See page #48) (Show one sample calculation and write answers for other two. asked by Mar on May 26, 2015; statistics. Hope-weeks (CHEM 1107) All Study Materials from Chemistry 1107. EESC *1010 The Dynamic Earth. College Publishing, 2017. Recognize the characteristics of chemical equilibrium. What is a Scientist? A scientist is a person who works in and has expert knowledge of a particular field of science. If after taking this quiz, you find yourself missing too many questions, or you are not sure why certain answers are. Because neuroscience and behav ioral research is so diverse, and unique and ambiguous situations continue to arise as science advances, it is impossible for this report to provide specific guidance. HCM Time Management. Professor: G. The lab explores the concepts and techniques each of you will need most as you progress through the rest of your chemistry curriculum. East China Normal University. 7 and not worry about backwards-incompatible changes. Start studying Chem 111 Lab. Topics include, but are not limited to, the nature of science and the scientific method, chemistry for biology, cell structure, metabolism, reproduction and genetics, organisms, evolution theory, and classification of. Emphasizes interpreting and reporting of data. 25 Chemistry Knowledge of the composition, structure, and properties of substances and of the chemical processes and transformations that they undergo. Account successfully activated. The final rule requires employers in certain industries to electronically submit to OSHA injury and illness data that employers are already required to keep under existing OSHA. 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Topics include graphing, the linear, quadratic, and exponential families of functions, and inverse functions. 5) Setting up the colorimeter: Plug in the colorimeter into Channel 1 of the Logger Pro Interface Box. This allows the laboratory to see how their results compare with other laboratories using the same starting material. Edmund Optics ® remains operational, including our 24-hour product & application support. Are the paper documents handed in each week—the Report Form/Post lab questions—for the current week's experiments? NO. General Information. In this manual we record the date of the testing event, the grade received, and any corrective action taken. CHM 103 Introduction to Chemistry Laboratory (1) Corequisites: CHM 101. org for more information. Laboratory Activity: Teacher Notes. Molecular Diagnostics / Immunology. ISBN: 9781305957787. "Chemistry: Experimental Founda-. 2 4 V DC 9. (You are collecting data when there is an icon of a Runner in the upper left hand corner of the screen. Introduction. Publisher Full Text Moos R: Work Environment Scale Manual. Teachers who have awaited the appear- ance of this t,hird and final xuthorized re- vision of CHEM Stndy shall be rewarded. Formal lab reports must be word-processed on a computer (not a word-processing machine or typewriter). The structure contains which functional group aldehyde ketone amino carboxyl 3. It prepares you for the jobs of the future by teaching you about machinery design, energy productions, thermal and fluid systems, hydraulics, pneumatics, material science, instrumentation and controls, computer. YOU WILL NOT BE PERMITTED TO WORK ON PHOTOCOPIES, PAGES FORM THE ORGINAL LAB WILL BE SUBMITTED AS PART OF THE LAB REPORT. Throughout the chapters, David presents two features that reinforce the. Best Practices for Maintaining Quality in Molecular Diagnostics Gyorgy Abel, MD, PhD Director, Clinical Chemistry. List of question tags. While most of the colorimeters used in the chemistry department are the rounded colorimeters which calibrate with the press of a button, you may occasionally encounter an older version which requires manual calibration. Chair: Donovan C. Diagnostic labs. Laboratory Course The laboratory class is designed to illustrate some of the principles involving performing scientific measurements, handling chemicals, and performing chemistry experiments. Lectins are a class of carbohydrate-binding proteins. To learn more, see our tips on writing great. COLLEGE ALGEBRA. 5-DETERMINATION OF AN EQUILIBRIUM CONSTANT LABORATORY OBJECTIVES AND ASSESSMENTS 1. It explains why the study exists. In order to. Discussion (not included in the Chem 105 report) Answer any questions posed by the manual or instructor that are outside the experiment. The Information Technology Laboratory (ITL), one of six research laboratories within the National Institute of Standards and Technology (NIST), is a globally recognized and trusted source of high-quality, independent, and unbiased research and data. Molecular Diagnostics / Immunology. Chem 115 - General Chemistry I Laboratory. If you don't see any interesting for you, use our search form on bottom ↓. Digital pathology is a new technology and industry. REQUIRED TEXTS/MATERIALS. The intensity of the color of a solution is proportional to the concentration of the absorbing species. that pic you posted is a continuous column (a very different kettle of fish). CHEM 1105 Spring 2015 (50761) Syllabus CHEM 1105 SPRING 2016 (90176) Syllabus CHEM 1105 FALL 2016 (18731). Here we report identification of the transposon-located (Tn OtChr ) chromate resistance genes from the highly tolerant strain. 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Teachers who have awaited the appear- ance of this t,hird and final xuthorized re- vision of CHEM Stndy shall be rewarded. Good notes and study guides helps you study better not harder. Using the values above, if titration requires 1. 54×105 cg cg Average light bulb wattage 600. INSTRUCTIONAL METHODOLOGY: This course consists of a separate lecture and a laboratory section. Join CS 105 at Piazza. On this page you can read or download study and master study guide physical science download in PDF format. Brendan Gibbons edited | 11 minutes ago. • THEY WILL BE COLLECTED AT THE BEGINNING OF LAB. 3: 3: 0: COLLEGE ALGEBRA Prerequisite: Minimum grade of C in MAT 1033C or appropriate score on an approved assessment. 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Safety in the Chemistry Lab and Safety Agreement Safety Quiz Chemistry Lab Equipment Experiment 1 - Measurements Experiment 2 - Separation of a Mixture Experiment 3 - Flame Tests and Electron Configuration Experiment 4 - The Periodic Table - Atoms and Elements Experiment 5 - Double Replacement Reactions Experiment 6 - Empirical Formula of a Compound Experiment 7 - Reaction Stoichiometry and. Welcome to TxSmartBuy COVID-19 Purchasing Information for Vendors The State of Texas is seeking critical equipment and capacity for medical providers, such as personal protective equipment (PPE), alternate care sites, and infection-control products. Find career opportunities, educational resources and more. 5–DETERMINATION OF AN EQUILIBRIUM CONSTANT LABORATORY OBJECTIVES AND ASSESSMENTS 1. Basic concepts of algebra. CHM 103 Introduction to Chemistry Laboratory (1) Corequisites: CHM 101. Lesson plans are complete for all three courses. This is my first Chem course so I have no idea what the answers are, please help. Haines (936) 294-1530. Digital Lab Manual. The bZIP class Abscisic acid Responsive Element (ABRE)-binding factor, OSBZ8 (38. 2011) G0434: will be used to report very simple testing methods, such as dipsticks, cups, cassettes, and cards, that are interpreted visually, with the assistance of a scanner. It introduces students to many different laboratory practices and concepts that will be used in subsequent chemistry laboratory classes (CHEM 2470 and beyond) and in other laboratory situations in biology, pharmacy, and chemical engineering (just to name a few!). facilities or sites that test human specimens for health assessment or to diagnose, prevent, or treat disease. An exploratory human laboratory experiment evaluating vaporized cannabis in the treatment of neuropathic pain from spinal cord injury and disease. More than $18 million in annual expenditures results in research by graduate students, undergraduate students, and post-doctoral associates. Topics of lecture handouts include chemistry, cell biology, cancer and genetics. You, my friend, are made up of cells. Types of Absences 29 §1107. CSUS Department of Chemistry Experiment 1 Chem. In most animals and plants that have been studied, centromeres contain megabase-scale arrays of tandem repeats. 1 atm= 1105 Pa= 760 mmHg= 760 torr Atmospheric pressure can simply be measured by a barometer by balancing the weight of Temperature It is a measure of the thermal energy of molecules or atoms of a substance. It explains why the study exists. 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text:
Formality and splitting of real non-abelian mixed Hodge structures

Pridham, J. P.
Description
We define and construct mixed Hodge structures on real schematic homotopy types of complex projective varieties, giving mixed Hodge structures on their homotopy groups and pro-algebraic fundamental groups. We also show that these split on tensoring with the ring R[x] equipped with the Hodge filtration given by powers of (x-i), giving new results even for simply connected varieties. Thus the mixed Hodge structures can be recovered from cohomology groups of local systems, together with the monodromy action at the Archimedean place. As the basepoint varies, these all become real variations of mixed Hodge structure.
Comment: This paper has been withdrawn by the author. Withdrawn - superseded by sections 1-10 of arXiv:1104.1409; 71 pages, supersedes arXiv:math/0611686; v2 overhauled, main new results are Thm 3.10, Sections 7 & 8, & parts of Section 2
Keywords
Mathematics - Algebraic Geometry, Mathematics - Algebraic Topology, 14C30, 14F35, 32S35, 55P62

format: plain


text:
# Common collector - bias resistor?

[Original question: CCD output buffer; seemed best to make the transistor part a separate post]

Taken from Wikipedia, the circuit in Fig. 1 acts as a common collector (high input impedance - low output impedance, voltage buffer).

Fig. 1:

In my application, the devices' datasheet (a CCD chip) suggests buffering the output, like in Fig. 2. That is the same as the "classic" CC above, with the notable exception of the 130 Ohm resistor.

What is it used for? The one thing I can think of is to help with biasing, but how will that affect the equations given in Wikipedia?

Bonus question: How much non-linearity can be expected from a CC, roughly speaking?
Let's say the CCD's Vout (before the CC buffer) ranges from 0 - 12V.

Fig. 2:

• I first "flashed" towards $C_\text{BE}$ since this is a video circuit. But perhaps the simpler answer may be: (1) making sure that the base-emitter junction is fully off and the output passively pulled to ground if the base pin isn't connected; and, (2) a desired shift in the quiescent/average DC output point (which will also depend on the source impedance of what's driving it.) Perhaps you could provide more context? – jonk Jan 6 at 23:32
• @jonk: More context is in my initial post (link provided above), and in the CCDs' datasheet (KAF-8300, page 5 - 6). It says "To activate the output structure, an off-chip load must be added to the VOUT pin of the device, see fig. 5". – user2286339 Jan 7 at 0:06
• Can you define the Vb average dc and the source impedance for source current avail? – Sunnyskyguy EE75 Jan 7 at 2:15

How were the resistors' values chosen?

• No idea what I/O specs they had in mind, but linearity for 800mV biased at 6V with 150MHz BW for some load pF + DC load variable range perhaps 75 Ohms is possible with 400mW extra DC power.

• The advantage is being able to drive coax with a 75 Ohm termination.

Does the Iout of 5.4mA indicate it is acting as a constant current sink?

. Probably peak DC + AC current.

• Zout spec is 100 min 180 max ohms (Table 6)
• Signal 655 mV max Monochrome
• DC bias current + ac current. must be for 6Vdc + 330mVpk
• Cct input impedance is not that high 1.2k ohms

Why isn't the on-chip charge-to-voltage converter sufficient to drive off-chip loads?

• allows variable design flexibility

## My Theory of Operation

• 2 stage cascade common source FETs driving common emitter
• With Re= 680, it can drive 1k AC coupled and 150 Ohms DC couple with some attenuation.
• Zin 1,200 Ohms approx.
• positive feedback R is called emitter degeneration with raises input impedance a bit, by bootstrap gain ratio at expense of input attenuation. 150:1200 ohm source: load
• with xxx pF load this can also increase HF gain >1 making it unstable so the degeneration of input attenuation still causes high frequency peaking but with more gain margin., which may not be relevant

If necessary anyway, why do they recommend a rather crude transistor buffer rather than some sort of precision op-amp, acting as a voltage follower?

Op Amps may have a big problem with up to 159MHz signal bandwidth (Table 6) with phase shift 1st , amplitude 2nd. - But possible but not suggested.

simulate this circuit – Schematic created using CircuitLab

The output swing might only <650mV not 780mV for monochrome and less on certain colors.


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# Proof of the classical div-curl-lemma

let $1 = \frac{1}{p} + \frac{1}{q}$ as usual. Let $f \in L^p, g \in L^q$ be vector fields from $\mathbb R^n$ to itself.

Assume $div f = 0$ and there exists a function $G$ s.t. $\nabla G = g$. Then $f \cdot g \in \mathcal H^1$ is a Hardy space function.

Do you know where I can find a proof of this conclusion? I am aware of a paper by Coifman et al. "Compensated compactness and Hardy spaces", but I am not granted access to this journal. Hence I am looking for an alternative resource.

-
Do you have any sort of library available, or are looking for an online reference? What books have you tried? I bet one of Evans' "Partial Differential Equations," Grafakos' "Classical Fourier Analysis," or Stein's "Harmonic Analysis" have a proof. –  JavaMan Mar 29 '11 at 15:49
Hi @Martin, did you end up looking through those books? –  Glen Wheeler Apr 14 '11 at 7:35
you find it in the book "weak convergence methods...." by evans –  user34172 Jun 21 '12 at 14:09
arxiv.org/abs/0712.2133 may be relevant. –  Willie Wong Jun 21 '12 at 16:08

A remark on the div-curl lemma by P. G. Lemarié-Rieusset gives a complete proof of the result in greater generality, with $L^p-L^q$ replaced by a Calderón-Zygmund pair of Banach spaces.


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clock-setters {clock} R Documentation

Calendar setters

Description

This family of functions sets fields in a calendar vector. Each calendar has its own set of supported setters, which are documented on their own help page:

There are also convenience methods for setting certain components directly on R's native date and date-time types.

Some general rules about setting components on calendar types:

• You can only set components that are relevant to the calendar type that you are working with. For example, you can't set the quarter of a year-month-day type. You'd have to convert to year-quarter-day first.

• You can set a component that is at the current precision, or one level of precision more precise than the current precision. For example, you can set the day field of a month precision year-month-day type, but not the hour field.

• Setting a component can result in an invalid date, such as set_day(year_month_day(2019, 02), 31), as long as it is eventually resolved either manually or with a strategy from invalid_resolve().

• With sub-second precisions, you can only set the component corresponding to the precision that you are at. For example, you can set the nanoseconds of the second while at nanosecond precision, but not milliseconds.

Usage

set_year(x, value, ...)

set_quarter(x, value, ...)

set_month(x, value, ...)

set_week(x, value, ...)

set_day(x, value, ...)

set_hour(x, value, ...)

set_minute(x, value, ...)

set_second(x, value, ...)

set_millisecond(x, value, ...)

set_microsecond(x, value, ...)

set_nanosecond(x, value, ...)

set_index(x, value, ...)

Arguments

 x [object] An object to set the component for. value [integer] The value to set the component to. ... These dots are for future extensions and must be empty.

Details

You cannot set components directly on a time point type, such as sys-time or naive-time. Convert it to a calendar type first. Similarly, a zoned-time must be converted to either a sys-time or naive-time, and then to a calendar type, to be able to set components on it.

Value

x with the component set.

Examples

x <- year_month_day(2019, 1:3)

# Set the day
set_day(x, 12:14)

# Set to the "last" day of the month
set_day(x, "last")

[Package clock version 0.6.1 Index]


text:
# velocity of an electron through a potential difference

A cell is prepared by dipping a chromium rod in 1M Cr2(SO4)3 solution and an iron rod in 1M FeSO4 solution. Is there an equation that relates the electron's energy to voltage? Voltages much higher than the 100 V in this problem are typically used in electron guns. In fact, electricity had been in use for many decades before it was determined that the moving charges in many circumstances were negative. This is analogous to the fact that gravitational potential energy has an arbitrary zero, such as sea level or perhaps a lecture hall floor. For example, a 5000 V potential difference produces 5000 eV electrons. When a free positive charge q is accelerated by an electric field, such as shown in Figure 1, it is given kinetic energy. how much kg-weight should be suspended to produce 0.1% incr. This unit is the electron-volt (eV). The speed of waves... *Response times vary by subject and question complexity. What will be the standard EMF of the cell? Q: A person has far and near points of 84 cm and 15 cm, respectively. Cutting a hole in the negative plate allows it to escape. 1 eV = 1.6 x 10-19 J We'll assume the capacitor has a uniform field E, and a potential difference with a magnitude of: |ΔV| = Ed, where d is the plate separation. alert("Thank you for connecting with Byju’s! event.preventDefault(); For a better experience, please enable JavaScript in your browser before proceeding. The change in potential is ΔV = VB – VA = +12 V and the charge q is negative, so that ΔPE = qΔV is negative, meaning the potential energy of the battery has decreased when q has moved from A to B. The particle may do its damage by direct collision, or it may create harmful x rays, which can also inflict damage. (10 points) If an electron is accelerated through a potential difference of 1000V, determine its maximum velocity. Thus a motorcycle battery and a car battery can both have the same voltage (more precisely, the same potential difference between battery terminals), yet one stores much more energy than the other since ΔPE = qΔV. http://cnx.org/contents/031da8d3-b525-429c-80cf-6c8ed997733a/College_Physics. Entering the values for ΔPE and ΔV, we get, $q=\frac{-30.0\text{ J}}{+12.0\text{ V}}=\frac{-30.0\text{ J}}{+12.0\text{ J/C}}-2.50\text{ C}\\$. goog_report_conversion(window.location.href); More about Kevin and links to his professional work can be found at www.kemibe.com. $1\text{V}=1\frac{\text{J}}{\text{C}}\\$. The energy supplied by the battery is still calculated as in this example, but not all of the energy is available for external use. '&entry.1504835072=' + encodeURI(source);

Resolution of normal reaction in a smooth inclined plane. In terms of potential, the positive terminal is at a higher voltage than the negative. encodeURIComponent(number) + '&entry.1783895534=' + encodeURIComponent(place) + '&entry.1725388830=' + Use 1.60×10−19 C for the magnitude of the charge on an electron and 9.11×10−31 kg for the mass of an electron…

var finalUrl = baseUrl + query; Hint: when the electron in accelerated over the potential difference, its kinetic energy increases. To find the charge q moved, we solve the equation ΔPE = qΔV: $q=\frac{\Delta\text{PE}}{\Delta{V}}\\$. Median response time is 34 minutes and may be longer for new subjects. This unit is the electron-volt (eV). Inside the battery, both positive and negative charges move. By the end of this section, you will be able to: Figure 1. Calculate (a) the speed of the electron and (b) the radius of its path in the magnetic field. For example, work W done to accelerate a positive charge from rest is positive and results from a loss in PE, or a negative ΔPE. An electron is accelerated through a potential difference of 1000 volts.Its velocity is nearly The process is analogous to an object being accelerated by a gravitational field. Admission fee for ICSE curriculum at Greenwood High International School? 1 eV is the amount of energy associated with moving one electron through a potential difference of 1 volt. We can identify the initial and final forms of energy to be KEi = 0, $KE_{f}=\frac{1}{2}mv^2\\$, PEi = qV, and PEf = 0. location.reload(); That is, $\text{n}_{\text{e}}=\frac{-2.50\text{ C}}{-1.60\times10^{-19}\text{ C/e}^{-}}=1.56\times10^{19}\text{ electrons}\\$. As we have found many times before, considering energy can give us insights and facilitate problem solving. The energy per electron is very small in macroscopic situations like that in the previous example—a tiny fraction of a joule. The electrostatic or Coulomb force is conservative, which means that the work done on q is independent of the path taken. Locate the images for each of the following object ... Q: 1- (a) calculate the focusing power of cornea . (Assume that the numerical value of each charge is accurate to three significant figures.). It is much more common, for example, to use the concept of voltage (related to electric potential energy) than to deal with the Coulomb force directly. A 30.0 W lamp uses 30.0 joules per second. When a force is conservative, it is possible to define a potential energy associated with the force, and it is usually easier to deal with the potential energy (because it depends only on position) than to calculate the work directly. How do vaccine provide immunity against a disease ? The potential difference between points A and B, VB – VA, is defined to be the change in potential energy of a charge q moved from A to B, divided by the charge. The Young's Modulus of copper is 1.25x10^11N/m^2 A wire of this material has 1mm diameter. Similarly, an ion with a double positive charge accelerated through 100 V will be given 200 eV of energy. url: finalUrl, crossDomain: true, A positive charge released from beside the positive plate will accelerate towards the negative plate. In summary, the relationship between potential difference (or voltage) and electrical potential energy is given by $\Delta{V}=\frac{\Delta\text{PE}}{q}\\$ and ΔPE = qΔV. An electron is accelerated from rest by a potential difference of 350 V. It then enters a uniform magnetic field of magnitude 200 mT with its velocity perpendicular to the field. Note also that as a battery is discharged, some of its energy is used internally and its terminal voltage drops, such as when headlights dim because of a low car battery. The potential difference between points A and B, VB − VA, is thus defined to be the change in potential energy of a charge q moved from A to B, divided by the charge. Thanks How much energy does each deliver? If the voltage between two points is zero, can a test charge be moved between them with zero net work being done? Determine electric potential energy given potential difference and amount of charge. These simple relationships between accelerating voltage and particle charges make the electron volt a simple and convenient energy unit in such circumstances. Step 1: Identify the Equation of Interest You may recall that in everyday physics, the kinetic energy of an object in motion is equal to (0.5)mv 2 , where m equals mass and v equals velocity. An evacuated tube uses an accelerating voltage of 40 kV to accelerate electrons to hit a copper plate and produce x rays. There is a useful energy unit that's particularly applicable to accelerating electrons, protons, or ions. The branch of chemistry in which we study about carbon and its compound is known as: The salt which is least likely to be found in mineral is. chemistry. 1. Part A What potential difference is needed to stop an electron that has an initial velocity v=5.6×105m/s? So if a charge of e coulombs is moved through a potential difference of V volts then the work done is eV Joules. Voltage is not the same as energy. It follows that an electron accelerated through 50 V is given 50 eV. The change in potential energy ΔPE is crucial, and so we are concerned with the difference in potential or potential difference ΔV between two points, where, $\displaystyle\Delta{V}=V_{\text{B}}-V_{\text{A}}=\frac{\Delta{\text{PE}}}{q}\\$. We use the letters PE to denote electric potential energy, which has units of joules (J). method: 'POST', Since the battery loses energy, we have ΔPE = –30.0 J and, since the electrons are going from the negative terminal to the positive, we see that ΔV = +12.0V. Mechanical energy is the sum of the kinetic energy and potential energy of a system; that is, KE+PE = constant. return false; Q: I'm having a hard time figuring out which equation I need to be using to plug in the data into the t... Q: Earth is about 150 million kilometers from the Sun (1 Astronomical Unit, or AU), and the apparent br... Q: A 1250 W radiant heater is constructed to operate at 115 V. (a) What is the current in the heater wh... Q: an electron accelerated from rest through potential difference V1 1.00 kV enters the gap between two... A: The equation for the kinetic energy of the electron is given by. There are, for example, calories for food energy, kilowatt-hours for electrical energy, and therms for natural gas energy. For conservative forces, such as the electrostatic force, conservation of energy states that mechanical energy is a constant. Since energy is related to voltage by ΔPE = qΔV, we can think of the joule as a coulomb-volt.


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# Harmonic Oscillator, overlap in states

1. May 23, 2014

### unscientific

1. The problem statement, all variables and given/known data

Particle originally sits in ground state about x=0. Equilibrium is suddenly shifted to x=s. Find probability of particle being in new first excited state.

2. Relevant equations

3. The attempt at a solution

Shifted wavefunctions are for ground state: $\phi'_0 = \frac{\alpha^{\frac{1}{2}}}{\pi^{\frac{1}{4}}} e^{ -\frac{\alpha^2}{2}(x-s)^2}$ and for first excited state: $\phi'_1 = \frac{2\alpha^{\frac{3}{2}}}{\pi^{\frac{1}{4}}} (x-s) e^{-\frac{\alpha^2}{2} (x-s)^2}$.

When the equilibrium is shifted to x=s, the particle's ground state at x=0 wavefunction becomes:

$$\phi'_{0(0)} = \frac{\alpha^{\frac{1}{2}}}{\pi^{\frac{1}{4}}} e^{-\frac{\alpha^2}{2}s^2}$$

To find probability of it being in first excited state, we overlap it with the first excited state:

$$\langle \phi'_1|\phi'_{0(0)}\rangle$$
$$= \frac{2\alpha^2}{\pi^{\frac{1}{2}}} e^{-\frac{(\alpha s)^2}{2}} \int_{-\infty}^{\infty}(x-s) e^{-\frac{\alpha^2}{2}(x-s)^2 } dx$$
$$= \frac{2\alpha^2}{\pi^{\frac{1}{2}}} e^{-\frac{(\alpha s)^2}{2}} \left[ \int_{-\infty}^{\infty} (x-2s)e^{-\frac{\alpha^2}{2}(x-s)^2} dx + \int_{-\infty}^{\infty}s \space e^{-\frac{\alpha^2}{2}(x-s)^2} \right] dx$$

Now, we let $2s = b$ and $a = \frac{\alpha}{\sqrt 2}$ and change $x$ to $x-s$ for the second integral:

$$=\frac{2\alpha^2}{\pi^{\frac{1}{2}}} e^{-\frac{(\alpha s)^2}{2}} \left[ -\frac{(2s)\pi^{\frac{1}{2}}}{\sqrt 2 \alpha} dx + s \int_{-\infty}^{\infty} e^{-\frac{\alpha^2}{2}x'^2} dx' \right]$$

$$=\frac{2\alpha^2}{\pi^{\frac{1}{2}}} e^{-\frac{(\alpha s)^2}{2}} \left[ -\frac{\sqrt 2 \pi^{\frac{1}{2}}s}{\alpha} + s\pi^{\frac{1}{2}} \frac{\sqrt 2}{\alpha} \right]$$

$$= 0$$

Last edited: May 23, 2014
2. May 23, 2014

### dauto

What you're looking for is $\langle \phi'_1|\phi_{0}\rangle^2$

3. May 23, 2014

### unscientific

Why is it $\phi_0$ and not $\phi_0'$?

4. May 23, 2014

### dauto

Because the particle was in the state $\phi_0$, not $\phi_0'$

5. May 24, 2014

### unscientific

Got it, thanks!

6. May 25, 2014

### unscientific

I did that, and I got an answer of $2(\alpha s)^2$..


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<meta http-equiv="refresh" content="1; url=/nojavascript/"> Discrete Random Variables ( Read ) | Probability | CK-12 Foundation
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# Discrete Random Variables

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Discrete Random Variables

What do you think the probability is that it will rain on Monday? You watched the weather forecast yesterday and the meteorologist said that the probability is 100% certain that it will rain on Monday and about 75% chance of rain on Tuesday. Could the probability of rain ever be described by 200%? What about 12%?

### Watch This

First watch this video to learn about discrete random variables.

Then watch this video to see some examples.

Watch this video for more help.

### Guidance

In previous Concepts, we looked at the mathematics involved in probability events. We looked at examples of event $A$ occurring if event $B$ had occurred (conditional events), of event $B$ being affected by the outcome of event $A$ (dependent events), and of event $A$ and event $B$ not being affected by each other (independent events). We also looked at examples where events cannot occur at the same time (mutually exclusive events), or when events were not mutually exclusive and there was some overlap, so that we had to account for the double counting (mutually inclusive events). If you recall, we used Venn Diagrams (below), tree diagrams, and even tables to help organize information in order to simplify the mathematics for the probability calculations.

Our examination of probability, however, began with a look at the English language. Although there are a number of differences in what terms mean in mathematics and English, there are a lot of similarities as well. We saw this with the terms independent and dependent. In this and the following Concepts, we are going to learn about variables. In particular, we are going to look at discrete random variables. When you see the sequence of words discrete random variables , it may, at first, send a shiver down your spine, but let’s look at the words individually and see if we can "simplify" the sequence!

The term discrete, in English, means to constitute a separate thing or to be related to unconnected parts. In mathematics, we use the term discrete when we are talking about pieces of data that are not connected. Random, in English, means to lack any plan or to be without any prearranged order. In mathematics, the definition is the same. Random events are fair, meaning that there is no way to tell what outcome will occur. In the English language, the term variable means to be likely to change or subject to variation. In mathematics, the term variable means to have no fixed quantitative value.

Now that we have seen the 3 terms separately, let’s combine them and see if we can come up with a definition of a discrete random variable. We can say that discrete variables have values that are unconnected to each other and have variations within the values. Think about the last time you went to the mall. Suppose you were walking through the parking lot and were recording how many cars were made by Ford. The variable is the number of Ford cars you see. Therefore, since each car is either a Ford or it is not, the variable is discrete. Also, random variables are simply quantities that take on different values depending on chance, or probability. Thus, if you randomly selected 20 cars from the parking lot and determined whether or not each was manufactured by Ford, you would then have a discrete random variable.

Now let’s define discrete random variables. Discrete random variables represent the number of distinct values that can be counted of an event. For example, when Robert was randomly chosen from all the students in his classroom and asked how many siblings there are in his family, he said that he has 6 sisters. Joanne picked a random bag of jelly beans at the store, and only 15 of 250 jelly beans were green. When randomly selecting from the most popular movies, Jillian found that Iron Man 2 grossed 3.5 million dollars in sales on its opening weekend. Jack, walking with his mom through the parking lot, randomly selected 10 cars on his way up to the mall entrance and found that only 2 were Ford vehicles.

The probability of a discrete random variable can range anywhere from 0 to 1. The less likely a discrete random variable is to occur, the closer the probability will be to 0, and the more likely a discrete random variable is to occur, the closer the probability will be to 1.

#### Example A

Which of the following can be represented by a discrete random variable?

a. The heights of the students in a high school

b. The number of sit-ups that you can do

c. The distances between stars in a galaxy

d. The number of wins by a professional hockey team

e. The speeds of the cars in a race

The heights of the students in a high school cannot be represented by a discrete random variable, since a height can take on any value within a certain range. For example, a height could be 64 inches, 64.5 inches, 64.55 inches, 64.555 inches, and so on. On the other hand, the number of sit-ups that you can do can be represented by a discrete random variable, because the number will always be an integer. The distances between stars in a galaxy are similar to the heights of the students in a high school in that there are an infinite number of possibilities, so these distances cannot be represented by a discrete random variable. However, the number of wins by a professional hockey team is similar to the number of sit-ups that you can do in that the number will always be an integer, so this number can be represented by a discrete random variable. Finally, the speeds of the cars in a race can take on any values, such as 100 MPH, 100.1 MPH, 100.12 MPH, 100.123 MPH, and so on, so these speeds cannot be represented by a discrete random variable. In summary, the answers to this question are as follows:

a. Cannot be represented by a discrete random variable

b. Can be represented by a discrete random variable

c. Cannot be represented by a discrete random variable

d. Can be represented by a discrete random variable

e. Cannot be represented by a discrete random variable

#### Example B

It is very likely, but not certain, that the high temperature will exceed $75^\circ \text{F}$ every day next week. Suppose that the discrete random variable $X$ represents the number of days next week that the high temperature will exceed $75^\circ \text{F}$ . Which of these could be $P(X=7)$ ?

a. $P(X=7)=0$

b. $P(X=7)=0.14$

c. $P(X=7)=0.5$

d. $P(X=7)=0.96$

e. $P(X=7)=1$

If the probability of an event is 0, it is impossible, and if the probability of the event is 1, it is certain. In this case, it is very likely, but not certain, that the high temperature will exceed $75^\circ \text{F}$ every day next week, so the probability will be close to 1, but not 1. Therefore, $P(X=7)$ could be equal to 0.96, so the correct answer is d.

#### Example C

Suppose that the discrete random variable $X$ represents the number of points out of 100 that Royce scores on a test. If $P(X=42)=0.88$ , which of these statements is most likely true?

a. Royce is likely to do well on the test.

b. Royce doesn't even know a single correct answer on the test.

c. Royce didn't study much for the test.

d. Royce knows all the correct answers on the test.

e. Royce studied a lot for the test.

Since $P(X=42)=0.88$ , the probability is high that Royce will get a low score on the test. However, if Royce gets 42 points out of 100, he at least knows some correct answers on the test. Therefore, the statement that is most likely true is that Royce didn't study much for the test, so the correct answer is C.

### Guided Practice

Put the following statements in order from least likely to most likely.

a. If a die is rolled 2 times, the same number will come up each time.

b. Christmas will be in December next year.

c. A letter chosen at random from the alphabet will be a consonant.

d. If a couple has a baby, it will be a girl.

e. The population of Wyoming will be greater than that of California in 10 years.

Let's look at each statement individually. The first statement is, "If a die is rolled 2 times, the same number will come up each time." The probability of this statement can actually be calculated to be $\frac{1}{6}$ . Next, we have, "Christmas will be in December next year." This probability of this statement is extremely high, as Christmas has traditionally been in December every year. After this, we have, "A letter chosen at random from the alphabet will be a consonant." Since 21 out of 26 letters in the alphabet are consonants, the probability of this statement is $\frac{21}{26}$ . The next statement is, "If a couple has a baby, it will be a girl." The probability of this statement will be about $\frac{1}{2}$ , since a boy and a girl are almost equally likely. Finally, we have, "The population of Wyoming will be greater than that of California in 10 years." The probability of this statement is extremely low, as the population of California is currently about 37,000,000, while the population of Wyoming is less than 600,000. In summary, here are our probabilities:

a. $\frac{1}{6}$

b. Extremely high

c. $\frac{21}{26}$

d. About $\frac{1}{2}$

e. Extremely low

Therefore, the order of the statements from least likely to most likely is e, a, d, c, b.

### Practice

1. Match the following statements from the first column with the probability values in the second column.
Probability Statement $P(X)$
a. The probability of this event will never occur. $\underline{\;\;\;\;\;} \ P(X) = 1.0$
b. The probability of this event is highly likely. $\underline{\;\;\;\;\;} \ P(X) = 0.33$
c. The probability of this event is very likely. $\underline{\;\;\;\;\;} \ P(X) = 0.67$
d. The probability of this event is somewhat likely. $\underline{\;\;\;\;\;} \ P(X) = 0.00$
e. The probability of this event is certain. $\underline{\;\;\;\;\;} \ P(X) = 0.95$
1. Match the following statements from the first column with the probability values in the second column.
Probability Statement $P(X)$
a. I bought a ticket for the State Lottery. The probability of a successful event (winning) is likely to be: $\underline{\;\;\;\;\;} \ P(X) = 0.80$
b. I have a bag of equal numbers of red and green jelly beans. The probability of reaching into the bag and picking out a red jelly bean is likely to be: $\underline{\;\;\;\;\;} \ P(X) = 0.50$
c. My dad teaches math, and my mom teaches chemistry. The probability that I will be expected to study science or math is likely to be: $\underline{\;\;\;\;\;} \ P(X) = 0.67$
d. Our class has the highest test scores in the State Math Exams. The probability that I have scored a great mark is likely to be: $\underline{\;\;\;\;\;} \ P(X) = 1.0$
e. The Chicago baseball team has won every game this season. The probability that the team will make it to the playoffs is likely to be: $\underline{\;\;\;\;\;} \ P(X) = 0.01$
1. Read each of the following statements and match the following words to each statement. You can put your answers directly into the table. Here is the list of terms you can add:
• certain or sure
• impossible
• likely or probable
• unlikely or improbable
• maybe
• uncertain or unsure
Statement Probability Term
Tomorrow is Friday.
I will be in New York on Friday.
It will be dark tonight.
It is snowing in August!
China is cold in January.
1. Read each of the following statements and match the following words to each statement. You can put your answers directly into the table. Here is the list of terms you can add:
• certain or sure
• impossible
• likely or probable
• unlikely or improbable
• maybe
• uncertain or unsure
Statement Probability Term
I am having a sandwich for lunch.
I have school tomorrow.
I will go to the movies tonight.
January is warm in New York.
My dog will bark.
1. Can the amount of lemonade in a pitcher be represented by a discrete random variable? Why or why not?
2. Can the number of musicians in an orchestra be represented by a discrete random variable? Why or why not?
3. Can the weights of the alligators in a swamp be represented by a discrete random variable? Why or why not?
4. Can the number of tickets sold to a movie be represented by a discrete random variable? Why or why not?
5. Give an example of something that can be represented with a discrete random variable. Explain your answer.
6. Give an example of something that cannot be represented with a discrete random variable. Explain your answer.


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# Problem: The rate of effusion of a particular gas was measured and found to be 24.0 mL/min. Under the same conditions, the rate of effusion of pure methane (CH4) gas is 47.8 mL/min. What is the molar mass of the unknown gas?

###### FREE Expert Solution

Recall that Graham's Law of Effusion allows us to compare the rate of effusion of two gases. Graham's Law states that the rate of effusion of a gas is inversely proportional to its molar mass.

$\mathbf{rate}\mathbf{=}\frac{\mathbf{1}}{\sqrt{{\mathbf{MM}}_{\mathbf{gas}}}}$

This means that when comparing two gases:

###### Problem Details

The rate of effusion of a particular gas was measured and found to be 24.0 mL/min. Under the same conditions, the rate of effusion of pure methane (CH4) gas is 47.8 mL/min. What is the molar mass of the unknown gas?


text:
# How large is the smallest object that can be detected at a given wavelength?

+ 3 like - 0 dislike
769 views

What is the cross section of the smallest object that can be detected with say visible light ($\lambda$ ~380 - 750 nm) or X - band radar ($\lambda$ ~20 - 50 mm).

Does the object need to have one side larger then $\frac{\lambda}{2}$ or something like that to get a reflection?

This post imported from StackExchange Physics at 2014-04-01 16:23 (UCT), posted by SE-user Theodor
detect how? for exemple for visible light: just visible againt the light or for example optical microscopy? that changes things

This post imported from StackExchange Physics at 2014-04-01 16:23 (UCT), posted by SE-user Steve
@steve - Ok, say rather then detect, say reflect.

This post imported from StackExchange Physics at 2014-04-01 16:23 (UCT), posted by SE-user Theodor
I would say rather than detect or reflect, "affect," since this is what we usually mean by measure.

This post imported from StackExchange Physics at 2014-04-01 16:23 (UCT), posted by SE-user Jeremy
It is of the same order as the wavelength

This post imported from StackExchange Physics at 2014-04-01 16:23 (UCT), posted by SE-user user1708

+ 5 like - 0 dislike

Seems like in principle, there should be no minimum size. For example, a small hand-held radio (cell phone for those of you in the 21st century) can detect, generate, and scatter EM waves with wavelength much longer than the object itself.

For optical and X-ray scales, one would probably be limited by quantum or thermal effects, which may in principle be mitigated at very low temperatures. But even so, a single atom is MUCH MUCH smaller than 500nm, and can absorb and emit light at that wavelength.

This post imported from StackExchange Physics at 2014-04-01 16:23 (UCT), posted by SE-user Jeremy
answered Dec 21, 2010 by (505 points)
I think Jeremy is correct. An object many times smaller than the wavelength can still cause scattering or absorption, so it would create a detectable change to the incident beam of light, which is all we need for detection. The quantum efficiency (what fraction of photons are scattered) will be small, but as long as a few are, the particle is detectable. Think of the blue sky. The air molecules are only a few angstroms size, whereas light with wavelengths of a few thousand angstroms do suffer from Rayleigh scattering. And we see this as blue sky, as the blue is scattered more than the red.

This post imported from StackExchange Physics at 2014-04-01 16:23 (UCT), posted by SE-user Omega Centauri
is incorrect in saying that "there should be no minimum size." The question is not whether light can be scattered by an object, but whether light of a given wavelength can resolve an object of a certain size - at least that is how I interpret it.

This post imported from StackExchange Physics at 2014-04-01 16:23 (UCT), posted by SE-user user346
"What is the cross section of the smallest object that can be detected"--That sure sounds more like scattering than resolving to me!

This post imported from StackExchange Physics at 2014-04-01 16:23 (UCT), posted by SE-user Jeremy
Indeed, the question was very clearly about detection, not resolution.

This post imported from StackExchange Physics at 2014-04-01 16:23 (UCT), posted by SE-user Colin K
+ 1 like - 0 dislike

Detecting an object requires you to get enough of a signal from it that you can discriminate that signal from background noise. This is not necessarily dependent on the size of the object, although it can be.

For example, if you are trying to detect an object which has very low reflectivity at your given wavelength, you might get a stronger signal if the object is larger. Of course this also depends on the geometry of the object, and how much of the reflected light is reflected towards your detector. Ultimately the deciding factor in whether you can detect an object is the ratio of the signal strength to the noise in your detection system. Engineers typically call this the "Signal to noise ratio" or SNR.

The Rayleigh limit will describe the minimum distance between two point sources such that an imaging system can distinguish one point from the other, rather than seeing them as a single point. However, this has nothing to do with the fundamental requirement of detecting the presence of an object in the first place. It is quite possible to, for example, detect medium-wavelength infrared light (with a wavelength of 3 to 8 microns) emanating from a pinhole or the tip of an optical fiber which is only a couple microns across. In this case an imaging system would indeed see a spot of light with a radius given by:

$$\begin{array}{rl} \Delta l = 1.22 \frac{f\lambda}{D} &\mbox{for a circular aperture}\\ \Delta l = \frac{f\lambda}{D} &\mbox{for a square aperture} \end{array}$$

Simply by detecting this spot, you would have detected the presence of the object, although you would not be able to say anything about its size or shape, because it is below the resolution of your device.

A good way to think about this is to get away from the concept of an imaging system. Imagine you've got a lens focusing light onto a photodiode, instead of an imaging detector like the CCD in a camera. With a single photodiode, you can't determine the size or shape of anything. All you can do is detect a signal, or the lack of a signal. This is mostly independent of resolving power or the size of the object being detected.

This post imported from StackExchange Physics at 2014-04-01 16:23 (UCT), posted by SE-user Colin K
answered Dec 27, 2010 by (10 points)
+ 0 like - 0 dislike

The Rayleigh criterion determines the maximum minimum size of objects - in terms of the maximum minimum angular resolution $\theta$ - which can be resolved at a give wavelength $\lambda$ and with a lens of a given diameter $D$:

$$sin(\theta) = 1.22 \frac{\lambda}{D}$$

The spatial resolution is given by:

$$\Delta l = 1.22 \frac{f\lambda}{D}$$

where $f$ is the focal length. For visible light this gives a limit of $\sim$ 200 nm for the minimum resolvable distance.

Of course, this is all based on classical optics. With newer metamaterial based lenses one can do much better than the Rayleigh limit.

This post imported from StackExchange Physics at 2014-04-01 16:23 (UCT), posted by SE-user user346
answered Dec 21, 2010 by (1,985 points)
Where is the magic number 1.22 come from? Is it like $\pi^2/8$ or something?

This post imported from StackExchange Physics at 2014-04-01 16:23 (UCT), posted by SE-user ja72
@jalexiou: "1.220 is approximately the first zero of the Bessel function of the first kind, of order one (i.e. J1), divided by π." from the wiki

This post imported from StackExchange Physics at 2014-04-01 16:23 (UCT), posted by SE-user hwlau
don't you mean "minimum size" and "minimum angular resolution"?

This post imported from StackExchange Physics at 2014-04-01 16:23 (UCT), posted by SE-user Jeremy
@jeremy, thanks for the corrections !

This post imported from StackExchange Physics at 2014-04-01 16:23 (UCT), posted by SE-user user346
While the equations are correct, the question clearly talks about reflection and detection, not resolution. Which would change the answer completely.

This post imported from StackExchange Physics at 2014-04-01 16:23 (UCT), posted by SE-user Bruce Connor
Yes, but the question of what can be "detected" is far too broad to answer coherently. Also the OP clearly says: "Does the object need to have one side larger then $\lambda/2$ or something like that to get a reflection?" - sounds to me like he is speaking of something more than just detection.

This post imported from StackExchange Physics at 2014-04-01 16:23 (UCT), posted by SE-user user346
Isn't that only true if you ignore near-filed effects? I recall that some years ago this limit was beaten by near-field microscopy.

This post imported from StackExchange Physics at 2014-04-01 16:23 (UCT), posted by SE-user Lagerbaer

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text:
Contest Duration: - (local time) (100 minutes) Back to Home
F - Making Palindrome /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

また、どのように選んでも回文を作ることが不可能である場合は -1 を出力してください。

### 制約

• 1 \leq N \leq 50
• 1 \leq |S_i| \leq 20
• S_i は英小文字から成る
• 1 \leq C_i \leq 10^9

### 入力

N
S_1 C_1
S_2 C_2
:
S_N C_N

### 入力例 1

3
ba 3
abc 4
cbaa 5

### 出力例 1

7

ba, abc, cbaa があります。

コスト 7 未満で回文を作ることはできないので、7 を出力してください。

### 入力例 2

2
abcab 5
cba 3

### 出力例 2

11

abcab1 個、cba2 個選んで、abcab, cba, cba の順で連結すると回文になり、コストは 11 です。

### 入力例 3

4
ab 5
cba 3
a 12
ab 10

### 出力例 3

8

a1 個だけ選んで回文とすることもできますが、abcba を選んで連結する方がコストが小さいです。

### 入力例 4

2
abc 1
ab 2

### 出力例 4

-1

Score : 600 points

### Problem Statement

We have N strings of lowercase English letters: S_1, S_2, \cdots, S_N.

Takahashi wants to make a string that is a palindrome by choosing one or more of these strings - the same string can be chosen more than once - and concatenating them in some order of his choice.

The cost of using the string S_i once is C_i, and the cost of using it multiple times is C_i multiplied by that number of times.

Find the minimum total cost needed to choose strings so that Takahashi can make a palindrome.

If there is no choice of strings in which he can make a palindrome, print -1.

### Constraints

• 1 \leq N \leq 50
• 1 \leq |S_i| \leq 20
• S_i consists of lowercase English letters.
• 1 \leq C_i \leq 10^9

### Input

Input is given from Standard Input in the following format:

N
S_1 C_1
S_2 C_2
:
S_N C_N

### Output

Print the minimum total cost needed to choose strings so that Takahashi can make a palindrome, or -1 if there is no such choice.

### Sample Input 1

3
ba 3
abc 4
cbaa 5

### Sample Output 1

7

We have ba, abc, and cbaa.

For example, we can use ba once and abc once for a cost of 7, then concatenate them in the order abc, ba to make a palindrome. Also, we can use abc once and cbaa once for a cost of 9, then concatenate them in the order cbaa, abc to make a palindrome.

We cannot make a palindrome for a cost less than 7, so we should print 7.

### Sample Input 2

2
abcab 5
cba 3

### Sample Output 2

11

We can choose abcab once and cba twice, then concatenate them in the order abcab, cba, cba to make a palindrome for a cost of 11.

### Sample Input 3

4
ab 5
cba 3
a 12
ab 10

### Sample Output 3

8

We can choose a once, which is already a palindrome, but it is cheaper to concatenate ab and cba.

### Sample Input 4

2
abc 1
ab 2

### Sample Output 4

-1

We cannot make a palindrome, so we should print -1.