ZuoTi.Pro
Question


3-6. Use either the expression for (E) in Example 3-1 or the one in Problem 3-5 to show that hy B

and that (E)-→ 0 T→00 as

referencing:

Postulate That the Average Ensemble Energy Is Equal to the Observed Energy of a System ls EXAMPLE 3-1 uation for (E) for the simple system of a (bare) proton in a magnetic eld B ON: The energy of a bare proton in a magnetic field B, is given by Ey y is a quantity called the magnetogyric ratio. The partition function of 干Ihy8, where consists of just two terms The average energy is obtained from either Equation 3.20 or 3.21: a In Q This expression for (E) (in units of hy B,/2) is plotted against T (in units of hy B./2kg in Figure 3.2. Note that (E) →-hyBz/2 as T → 0 and that (E) → 0 as T → oo. As T0, there is no thermal energy, so the proton orients itself parallel to the magnetic field with certainty. As T → oo, however, the thermal energy of the proton increases to such an extent that the proton is equally likely to point in either direction. TI (hyB,/2kB) 25 50iy restriction hples of bosons are alpha lIlS out that fermions and bosons constitute o the summation in Equation 3.37 for the case of fermions. n nature. We must recognize the occupancy requirements of all the known einback now to the summation in when we attempt to carry out the summation in Equation 3.37. and bosons when w thes cal fermions can occupy the same single-particle energy st Lets go back now cause no two identical ecauin which two or more es inrefore, the indice two identi e indices are the same cannot be included in the sum- s i, j, k, are not independent of one another, so of Equation 3.37 poses problems for the s mation V, T) by means direct evaluation of Q(N, V fermions EXAMPLE 3-5 with energies ε , in Equation 3.37. system of two noninteracting identical fermions, each of which has states e,, ε3, and ε4. Enumerate the allowed total energies in the summation SOLUTION: For this system i,j-1 of the 16 terms that would occur in an unrestricted evaluation of Q, only six are allowed for two identical fermions; these are the terms with energies

science   chemistry   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

expression avesHe enezgy ao it is 2. 2. 2te- 13 e-e -20 2 4)거 2 e. ,, スイ dl ㄚ Hope

0 0
Add a comment
Know the answer?
Add Answer to:
referencing: 3-6. Use either the expression for (E) in Example 3-1 or the one in Problem...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • 16 , Eo Problem 1 (8 pts): An experimentalist is examining a kind of non-interacting identical...

    16 , Eo Problem 1 (8 pts): An experimentalist is examining a kind of non-interacting identical particles that could be either spinless bosons or spin-half fermions by putting a number of them inside a potential and measuring the energy levels of the system, but without being able to resolve the degeneracy of each level. Energy levels do not depend on the particles' spin. The following values of the energy are observed: No particles: 0 -5€ 1 particle: E, 2E, 5E...

  • hat would be the partition function of this system according to equa tion 7.16? (e) W...

    hat would be the partition function of this system according to equa tion 7.16? (e) W (f) What is the probability of finding both particles in the same single-par state, for the three cases of distinguishable particles, identical bosons, ane identical fermions? 4) The entropy of a two-state para magnet is given by S = Nk [ln(2 cosh x )-x tanhx ]], where x 2 uB kT Find the value of S at T-0 and T-oo. sinhx = "(ex-c"); coshx-(ex...

  • Part B All this are multiple questions Part C Part D Part E Question 3 (MCQ...

    Part B All this are multiple questions Part C Part D Part E Question 3 (MCQ QUESTION) [8 Marks) A hypothetical quantum particle in 10 has a normalised wave function given by y(x) = a.x-1.b, where o and bare real constants and i = V-1. Answer the following: a) What is the most likely x-position for the particle to be found at? Possible answers forder may change in SAKAI 14] a - b + ib a 0 Question 3 (MCQ...

  • Question 1.) Use the worked example above to help you solve this problem. A balloon contains...

    Question 1.) Use the worked example above to help you solve this problem. A balloon contains 4.40 moles of a monatomic ideal gas. As energy is added to the system by heat (say, by absorption from the Sun), the volume increases by 25% at a constant temperature of 26.0°C. Find the work Wenv done by the gas in expanding the balloon, the thermal energy Q transferred to the gas, and the work W done on the gas. Wenv = ____J...

  • 8.4 The Two-Dimensional Central-Force Problem The 2D harmonic oscillator is a 2D central force pr...

    8.4 The Two-Dimensional Central-Force Problem The 2D harmonic oscillator is a 2D central force problem (as discussed in TZD Many physical systems involve a particle that moves under the influence of a central force; that is, a force that always points exactly toward, or away from, a force center O. In classical mechanics a famous example of a central force is the force of the sun on a planet. In atomic physics the most obvious example is the hydrogen atom,...

  • 1) Use the Energy-Interaction Model to explain whether the following statement is true or false

    1) Use the Energy-Interaction Model to explain whether the following statement is true or false: "A quantity of ice at 0℃ must contain less total energy than the same quantity of water at 0℃.2) According to the definition of heat in the online reading, can an energy system contain a certain amount of heat? Explain.3) Imagine that you place a piece of copper with an initial temperature of 20℃ in contact with some liquid water with an initial temperature of...

  • 3. (a) Ampère's law can be written in the following form: $6.d1= B.d = Hol. Use...

    3. (a) Ampère's law can be written in the following form: $6.d1= B.d = Hol. Use this to show that the magnetic field B inside a toroidal-shaped solenoid, with n turns per unit length and carrying a current I, has a magnitude equal to Monl. Explain how you result can be used to obtain the magnetic field inside a long straight solenoid, with n turns per unit length. {4} (b) Faraday's law can be written in the following form: $...

  • Problem 4: Evaluation of the convolution integral too y(t) = (f * h)(t) = f(t)h(t –...

    Problem 4: Evaluation of the convolution integral too y(t) = (f * h)(t) = f(t)h(t – 7)dt is greatly simplified when either the input f(t) or impulse response h(t) is the sum of weighted impulse functions. This fact will be used later in the semester when we study the operation of communication systems using Fourier analysis methods. a) Use the convolution integral to prove that f(t) *8(t – T) = f(t – T) and 8(t – T) *h(t) = h(t...

  • Mahiindra cole Centrale Tutorial Sheet-3 Central forces/SHM PHYSICS-101 Date 150220 1) Let a particle be subject to an attractive central force of the form n where r is the distance between the parti...

    Mahiindra cole Centrale Tutorial Sheet-3 Central forces/SHM PHYSICS-101 Date 150220 1) Let a particle be subject to an attractive central force of the form n where r is the distance between the particle and the centre of the force. Find fn), if all circular orbits are to have identical areal velocities, A 2) For what values of n are circular orbits stable with the potential energy un-Ai where A > 0? 3) A satellite of mass m 2,000 kg is...

  • some context Problem 3: Use simple kinetic theory of gases discussed in section 1.3.2 as well...

    some context Problem 3: Use simple kinetic theory of gases discussed in section 1.3.2 as well as Fourer's law of condustion to prove: 2 R373 D11 = 3113/202pm Dal We were unable to transcribe this imageof a nes. the xed the led negligible The following assumptions about the structure of the cases are made in order to investigate the statistical rules of the random motion of the molecules: The size of the gas molecules is negligible compared with the distance...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT