Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
expand_more
expand_more
format_list_bulleted
Question
Chapter 17, Problem 17.6E
Interpretation Introduction
Interpretation:
Stirling’s approximation equation is to be derived.
Concept introduction:
Stirling’s approximation is used to estimate the natural logarithm of factorial of a number. The Stirling’s approximation is represented as,
It is assumed in Stirling’s approximation that
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Identify the systems for which it is essential to include a factor of 1/N! on going from Q to q : (i) a sample of carbon dioxide gas, (ii) a sample of graphite, (iii) a sample of diamond, (iv) ice.
4. A one-particle, one-dimensional system has the state function.
1
e
y = sin(at) (2)
4:
32 1
+ cos (at) (2) 4 x
xe
Where a is a constant and c-2.000 Å. If the particle's position is measured at t=0,
estimate the probability that the result will between 2.000 Å and 2.0001 Å. (This
range can be thought of as infinitesimal process)
For the function:
R, a, b - are constant- Write an expression for the derivative of p in relation to v when the other quantities are constant- Write an expression for the derivative of p in relation to T when all other quantities are constant.
Chapter 17 Solutions
Physical Chemistry
Ch. 17 - Prob. 17.1ECh. 17 - Prob. 17.2ECh. 17 - Prob. 17.3ECh. 17 - Prob. 17.4ECh. 17 - Prob. 17.5ECh. 17 - Prob. 17.6ECh. 17 - Prob. 17.7ECh. 17 - Prob. 17.8ECh. 17 - Prob. 17.9ECh. 17 - Prob. 17.10E
Ch. 17 - Prob. 17.11ECh. 17 - If the ni values are all the same, a shorthand way...Ch. 17 - Prob. 17.13ECh. 17 - Prob. 17.14ECh. 17 - Prob. 17.15ECh. 17 - Prob. 17.16ECh. 17 - Prob. 17.17ECh. 17 - Prob. 17.18ECh. 17 - Prob. 17.19ECh. 17 - Prob. 17.20ECh. 17 - Prob. 17.21ECh. 17 - Prob. 17.22ECh. 17 - Explain why q is a constant for a given system at...Ch. 17 - What is the ratio of ground-state nickel atoms in...Ch. 17 - Ti3+ has the following electronic energy levels:...Ch. 17 - Using the fact that =1/kT, show that equations...Ch. 17 - A one-dimensional particle-in-a-box has a length...Ch. 17 - Prob. 17.28ECh. 17 - Prob. 17.29ECh. 17 - Prob. 17.30ECh. 17 - Prob. 17.31ECh. 17 - What is the value of q at absolute zero? Is it the...Ch. 17 - Prob. 17.33ECh. 17 - Prob. 17.34ECh. 17 - Prob. 17.35ECh. 17 - Prob. 17.36ECh. 17 - Prob. 17.37ECh. 17 - Prob. 17.38ECh. 17 - Prob. 17.39ECh. 17 - Prob. 17.40ECh. 17 - Prob. 17.41ECh. 17 - Prob. 17.42ECh. 17 - What change is there in the Sackur-Tetrode...Ch. 17 - Prob. 17.44ECh. 17 - Prob. 17.45ECh. 17 - Prob. 17.46ECh. 17 - Calculate the thermal de Broglie wavelength of He...Ch. 17 - Prob. 17.48ECh. 17 - Prob. 17.49ECh. 17 - Prob. 17.50ECh. 17 - Prob. 17.51ECh. 17 - Prob. 17.52ECh. 17 - Prob. 17.53ECh. 17 - Use equation 17.56 to determine the change in...Ch. 17 - For an electron that has a velocity of 0.01c where...Ch. 17 - Use the Sackur-Tetrode equation to derive the...Ch. 17 - Prob. 17.57ECh. 17 - Prob. 17.58E
Knowledge Booster
Similar questions
- What are the salient features of Aufbau principle?arrow_forwardOutline the principles behind the derivation of the Boltzmann distribution.arrow_forwardIdentify the systems for which it is essential to include a factor of 1/N! on going from Q to q : (i) a sample of helium gas, (ii) a sample of carbon monoxide gas, (iii) a solid sample of carbon monoxide, (iv) water vapour.arrow_forward
- Justify your answer:arrow_forwardThe Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose ? = 2.2 and ? = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250more than 300 (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) hrarrow_forwardThe answer for Kp= 12.9 and the answer for x=0.842. Please show me how to obtain this answersarrow_forward
- Consider the molecules: CH2=CH-CH=CH-CH=CH-CH=CH-CH=CH2. Let’s assume that the 10 electrons that make up the double bonds can exist everywhere along the carbon chains. The electrons can then be considered as particles in a box; the ends of the molecule correspond to the boundaries of the box with a finite or zero potential energy inside. In this “molecular box”, 2 electrons can occupy an energy level. What’s the smallest frequency of light that can excite the electron? Briefly explain why.arrow_forwardWe can use the classical harmonic oscillator to think about molecular bonds. The HCI molecule has a force constant k = 481 N/m. For the mass, use the reduced mass, which is defined as µ = (m₁m₂)/(m₁+m₂). a) Plot the potential energy of HCl from -1 to 1 Å. What happens to the curvature of the potential as the force constant is varied? What does this mean physically? b) Plot position as a function of time for a total energy of 6 x 10-20 J. What is the period of the motion? How does the period change as the force constant is varied? Explain why this makes sense physically.arrow_forwardEvaluate the following commutators d (a) | x, dx d (b) | х, dy d (c) dx d + x dx -arrow_forward
- The cohesive energy density, U, is defined as U/V, where U is the mean potential energy of attraction within the sample and V its volume. Show that U = 1/2N2∫V(R)dτ where N is the number density of the molecules and V(R) is their attractive potential energy and where the integration ranges from d to infinity and over all angles. Go on to show that the cohesive energy density of a uniform distribution of molecules that interact by a van der Waals attraction of the form −C6/R6 is equal to −(2π/3)(NA2/d3M2)ρ2C6, where ρ is the mass density of the solid sample and M is the molar mass of the molecules.arrow_forward4. The variance of many measurements of observable A is given by o = (A²) – (A)². Derive the variance in the measurements of position of a particle in a box in state „(x).arrow_forwardFor two nondegenerate energy levels separated by an amount of energy ε/k=500.K, at what temperature will the population in the higher-energy state be 1/2 that of the lower-energy state? What temperature is required to make the populations equal?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,
Physical Chemistry
Chemistry
ISBN:9781133958437
Author:Ball, David W. (david Warren), BAER, Tomas
Publisher:Wadsworth Cengage Learning,