By considering its constituents, determine the dimensions (e.g. length, distance over lime. etc.) of the denominator in equation(926). Why is the result sensible?

Short Answer

Expert verified

It follows that the denominator must be dimensionless so that the average energy also has units of energy

Step by step solution

01

Step 1:Equation (26)

Equation (26) writes:

N(E)D(E)dE

WhereNis the occupation number or simply the number of particles in a particular energy state,D(E)is the density of states anddEis the energy range.

02

Step 2:

In the above equation,N is dimensionless, D(E)has units of 1 /energy anddE has units of energy. Using dimensional analysis, equation (26) must therefore be dimensionless.

03

denominator must be dimensionless

This result is sensible because equation is one of the recipes to calculate the average energyE¯ Since the equation for average energy has numerator with units of energy, it follows that the denominator must be dimensionless so that the average energy also has units of energy.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The temperature of our Sun’s surface is ~6000K.(a) At what wavelength is the spectral emission of the Sun is maximum? (Refer to Exercise 79.) (b) Is there something conspicuous about this wavelength?

A "cold" subject,T1=300K, is briefly put in contact with s "hut" object,T2=400K, and60Jof heat flows frum the hot object io the cold use. The objects are then spiralled. their temperatures having changed negligibly due ko their large sizes. (a) What are the changes in entropy of each object and the system as a whole?

(b) Knowing only this these objects are in contact and at the given temperatures, what is the ratio of the probabilities of their being found in the second (final) state for that of their being found in the first (initial) state? What dies chis result suggest?

Consider a gas of atoms that might serve as a laser medium but that is inequilibrium, With no population inversions. A photon gas coexists with the atoms. Woulda photon whose energy is precisely the differencebetween two atomic energy states be more likely to be absorbed or to induce a stimulated emission or neither? We expect that inequilibrium the number. of atomsat different levels and the number of photons of a given energy should be stable. Is your answer compactible?

A. block has a cavity inside, occupied by a photon gas. Briefly explain what the characteristic of this gas should have to do with the temperature of the block.

Nuclear density is approximately 1017 kg/m3. (a) Treating them as a gas of fermions bound together by the (no electrostatic) "strung attraction." calculate EFfor the neutrons in lead-206 (82 protons and 124 neutrons). (b) Treating them the same way. what would EFbe for the protons? (c) In fact, the energies of the most energetic neutrons and protons, those at the Fermi energy, are essentially equal in lead-206? What has been left out of pars (a) or (b) that might account for this?

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free