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# For ultrarelativistic particles such as photons or ISBN: 9780201380279 40

## Solution for problem 13P Chapter A

An Introduction to Thermal Physics | 1st Edition

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Problem 13P

For ultrarelativistic particles such as photons or high-energy electrons, the relation between energy and momentum is not E = p2/2m but rather E = pc. (This formula is valid for massless particles, and also for massive particles in the limit E ≫ mc2.)

(a) Find a formula for the allowed energies of an ultrarelativistic particle confined to a one-dimensional box of length L .

(b) Estimate the minimum energy of an electron con lined inside a box of width 10−15m. It was once thought that atomic nuclei might cont ain electrons; explain why this would be very unlikely.

(c) A nucleon (proton or neutron) can be thought of as a bound state of three quarks that are approximately massless, held together by a very strong force that effectively confines them inside a box of width 10−15 m. Estimate the minimum energy of three such particles (assuming all three of them Lobe in the lowest-energy state), and divide by c2 to obtain an estimate of the nucleon mass.

Step-by-Step Solution:

Step 1 of 4</p>

(a) Find a formula for the allowed energies of an ultrarelativistic particle confined to a one-dimensional box of length L .

The given formula for energy of an ultrarelativistic particle is, Where E is energy which is quantized, P is momentum and c is speed of light.

The value of momentum is also quantized due to the property of wavelength quantization.

That is, Using the relation, where h is planck’s constant and is wavelength. Step 2 of 4</p>

The wavelength in terms of width L is given by Therefore, above equation becomes ………...1

Hence, the above formula gives the allowed energies of an ultrarelativistic particle confined to a one-dimensional box of length L

Step 3 of 4

Step 4 of 4

##### ISBN: 9780201380279

Since the solution to 13P from A chapter was answered, more than 240 students have viewed the full step-by-step answer. An Introduction to Thermal Physics was written by and is associated to the ISBN: 9780201380279. The answer to “For ultrarelativistic particles such as photons or high-energy electrons, the relation between energy and momentum is not E = p2/2m but rather E = pc. (This formula is valid for massless particles, and also for massive particles in the limit E ? mc2.)(a) Find a formula for the allowed energies of an ultrarelativistic particle confined to a one-dimensional box of length L .________________(b) Estimate the minimum energy of an electron con lined inside a box of width 10?15m. It was once thought that atomic nuclei might cont ain electrons; explain why this would be very unlikely.________________(c) A nucleon (proton or neutron) can be thought of as a bound state of three quarks that are approximately massless, held together by a very strong force that effectively confines them inside a box of width 10?15 m. Estimate the minimum energy of three such particles (assuming all three of them Lobe in the lowest-energy state), and divide by c2 to obtain an estimate of the nucleon mass.” is broken down into a number of easy to follow steps, and 164 words. The full step-by-step solution to problem: 13P from chapter: A was answered by , our top Physics solution expert on 07/05/17, 04:29AM. This full solution covers the following key subjects: Energy, ultrarelativistic, particles, box, estimate. This expansive textbook survival guide covers 10 chapters, and 454 solutions. This textbook survival guide was created for the textbook: An Introduction to Thermal Physics , edition: 1.

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For ultrarelativistic particles such as photons or

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