For a system of particles at room temperature, how large must € - μ be before the Fermi-Dirac, Bose-Einstein, and Boltzmann distributions agree within 1% ? Is this condition ever violated for the gases in our atmosphere? Explain.

For a system of particles at room temperature, how large must € - μ be before the Fermi-Dirac, Bose-Einstein, and Boltzmann distributions agree within 1% ? Is this condition ever violated for the gases in our atmosphere? Explain.

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter10: Statistical Physics

Section: Chapter Questions

Problem 10P

See similar textbooks

Related questions

Q: Suppose you have a "box" in which each particle may occupy any of 10 single-particle states. For…

A: To determine: Partition function if the box contains two identical fermions.

Q: The Fermi-Dirac statistic describes the probability of occupation of an energy state E, as a…

Q: Estimate the wavelength at which plasma reflection will occur for a metal having the density of…

Q: A. If the position of a chlorine ion in a membrane is measured to an accuracy of 1.50 µm, what is…

Q: What is the minimum possible temperature ? Is there also a maximum possible temperature?

A: Temperature can is defined as a phenomenon which occurs due to the vibration of molecules.Minimum…

Q: The Boltzmann distribution - not valid when the number of available states is small - may result in…

A: Two casses are given, for that we have to expalin reason wise

Q: E) Show that Equation µ(r) = A(1+c,r) exp () is a solution to Schrödinger Equation (Equation 2-5)…

A: The calculations for part (c) are shown below.

Q: What is the rms speed (Urms) of an He atom at 28C? Solve and explain

Q: A. (a) Consider a canonical ensemble having N particle, V volume and at T temperature. Write down…

A: The canonical partition function is an ensemble that deals with the closed system i.e. having the…

Q: Derive an expression of uncertainty (error) in P and determine 6P / P. Suppose the uncertainty in op…

Q: (a) If the position of a chlorine ion in a membrane is measured to an accuracy of 1.00 μm, what is…

A: Given, Mass, m=5.86×10-26 kg plank's constant, h=6.63×10-34 Js Position of a chlorine, ∆x=1×10-6 m…

Q: Show that Kp = 0.75 nM is a DG = -50.8 kJ/mol. Express DG in terms of pN nm Compare the force…

A: Given: KD=0.75 nM=0.75×10-9m ∆G=-50.8 kJ/mol

Q: Determine the heat capacity of a two-dimensional layer of atoms in the Debye model. As in the…

Q: Calculate the density of thermionic emission current in Cs at 500 ,1000 ,2000 k°.

A: The required density of thermionic emission current at 500 K is, The required density of thermionic…

Q: Give several p-type and n-type dopant for GaAs and ZnSe. What kind of dopant is Si in InP

A: In this question we have to give examples of p type and n type dopants. Please give positive…

Q: 1)A missile protection system consists of n radar sets operating independently, each with…

Q: Q6/ Discuss the probability f(E) of finding an electron in energy state, where f(E) is the Fermi…

Q: What is the probability that the electron tunnels through the barrier? (Use 9.11 10-31 kg for the…

A: Given data: The kinetic energy is: E = 3.10 eV The width of barrier is: L = 0.230 nm The mass of an…

Q: 1 A system Consists of 6000 particles 6000 particles j A system distribute d Consists of energy…

Q: Show that V (x) = 2 ln(tanh(x/2)) satisfies the Poisson– Boltzmann equation V"(x) = sinh(V (x)),…

A: Given, Vx =2×lntan hx2

Q: Calculate the threshold frequency of Gold with 7.8x10^-19 J Work Function.

A: The relation of the threshold frequency and the energy as φ=hν

Q: Q. No 02: a) Consider a system of two identical particles occupying any of three energy levels A, B…

Q: Let f(ɛ) be the Fermi-Dirac distribution function and µ be the chemical potential. Obtain the…

Q: In a two levels systems, the levels are separated by an energy E,-E,. find the ratio of population…

Q: Suppose your professor discovers dark matter, and it turns out to be a new type of subatomic…

Q: Calculate the ambipolar diffusion coefficient of intrinsic Ge at 350 K. p/p-2.1, -3900 cm² V-ls-¹. O…

Q: An experiment was conducted to find the relationship between the spec heat of Potassium metal and…

Q: Show that TV 32 Cp – Cy = %3D reduces to Cp-Cv = R for an ideal gas.

Q: The atoms in a solid possess a certain minimum zero-point energy even at 0 K, while no such…

A: According to the uncertainty principle, it is impossible to measure simultaneously both the position…

Q: For an ideal gas O2 at T = 293 K fi nd the two speeds v that satisfy the equation 2F(v) = F(v*).…

A: Given: An ideal gas of oxygen O2 Temperature: 293 [K] Maxwell`s distribution function: F(v) Mass of…

Q: Suppose that an energy level (j) includes 6 states (gj =6) and 3 particles (Nj =3). What will be the…

Q: 4c sin M ka The dispersion relation of phonons in a monatomic, linear chain of atoms is given by:…

A: The maximum phonon frequency at the edge of the Brillouin zone is, wmax = √(4C/M) , where M is the…

Q: Near the surface of a certain kind of star, approximately one hydrogen atom per 10 million is in the…

A: Given that near the surface of a certain kind of star, approximately one hydrogen atom per 10…

Q: Boltzmann distribution a) There are 1000 molecules are bouncing at 300K between two wells separated…

Q: The probability of finding an N2 molecule at ambient temperature at 515 m/s is zero. True or…

A: Required : True or False : The probability of finding an N2 molecule at ambient temperature at 515…

Question

For a system of particles at room temperature, how large must _€ - μ be before the Fermi-Dirac, Bose-Einstein, and Boltzmann distributions agree within 1% ? Is this condition ever violated for the gases in our atmosphere? Explain.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

Assume that the Maxwell-Boltzmann distribution is valid in a gas of atomic hydrogen. What is the relative number of atoms in the ground state and first excited state at 293 K (room temperature), 5000 K (the temperature at the surface of a star), and 106 K (a temperature in the interior of a star)?
The partition function of an ensemble at a temperature T is N Z = (2 cosh kgT where kg is the Boltzmann constant. The heat capacity of this ensemble at T = is X Nkg, where the value of X is %3D kB (up to two decimal places).
Q3. For a system at T = 300 K, what has to be the value of (ɛ - u) so that the distributions of Fermi- Dirac, Bose-Einstein, and Boltzmann agree to within 1%? Is this condition satisfied for gases in the atmosphere?
What is the root mean square velocity, vrms, for Helium atom (He) at 66oC? Hint: How many amu does an He atom contain? 1 amu = 1.67 x 10-27 kg Boltzman's Constant, k = 1.38 x 10-23 J/K Give your answer in m/s to 4 significant figures (NO DECIMALS)
Near the surface of a certain kind of star, approximately one hydrogen atom per 10 million is in the first excited level (n = 2). Assume that the other atoms are in the n = 1 level. Use this information to estimate the temperature there, assuming that Maxwell-Boltzmann statistics are valid.
Maxwell velocity distribution. Consider an ideal gas that obeys a Maxwell velocity distribution. Each particle has mass m. (a) Calculate the expected kinetic energy of a gas molecule using the Maxwell distribution. Could you have calculated the expected value another way? (b) Is your answer to part (a) equal to (i)mc² , (ii)mums , (ii) ;mup, none of these. Recall C is the average speed,Urms is the root-mean-square speed, and Ump is the most probable speed. Show your work. (c) If the temperature is held constant, but the mass m of each particle is increased by a factor of 4, by how much does your answer to (a) change? By how much does C change?
Calculate the Fermi-Dirac distribution frp (E) and the Maxwell-Boltzmann distribution fMB (E) for E = Ep, and E > Ep and E < Ep when the temperature T 0.
How does the Boltzmann distribution and statistics explain the behavior of an ideal gas in terms of the distribution of molecular energies and the probability of various energy states?
Q4/a/ Using the Fermi-Dirac probability function, explain the relationship of temperature with the energy levels that an electron can occupy compared to the Fermi level. Among all possible cases, reinforce the answer with mathematical equations.
For a system of particles at room temperature (300K), what value must & be before the Fermi-Dirac, Bose-Einstein, and Maxwell-Boltzmann distributions agree within 0.1% ? Justify your answer.
Problem 2) Consider the following Maxwell Boltzmann distribution of molecular speeds: P(v) = 4( m 27kBT. mp² v²e 2kgT To calculate average values for say f(v) (function of v) one just integrates f(v) with P(v)dv from zero to infinity = P(v)f(v)dv, where signifies average of f(v). Of course, the distribution should be normalized: P(v)dv=1, (is a requirement for any probability distribution). a) Check the last equation. b) Calculate the average of v. c) Calculate the average of v². d) Calculate from c) the RMS value of the speed. e) Calculate the most probable value of v. f) Square the results of b, d and e and rank them from smallest to the largest value.
. . Maxwell -Boltzman speed distribution is given by nu)dU=A e 2KT 2dv a) find A by Using the condition n(v)du where N is the number of porticles. b) Using the Speed distribution in question de termine the speed that has the maximum probability.