Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
9th Edition
ISBN: 9781305932302
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 40, Problem 1OQ
To determine

Rank the wavelengths of the given quantum particles from the largest to smallest.

Expert Solution & Answer
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Answer to Problem 1OQ

The ranking of the wavelengths of the quantum particles is d>a=e>b>c_.

Explanation of Solution

The given particles are,

  1. (a) A photon with kinetic energy of 3eV.
  2. (b) An electron with kinetic energy 3eV.
  3. (c) A proton with kinetic energy 3eV.
  4. (d) A photon with kinetic energy of 0.3eV.
  5. (e) An electron with momentum 3eVc.

Write the expression for the wavelength of the quantum particle.

λ=hp (I)

Here, λ is the wavelength of the quantum particle, h is the Planck’s constant, and p is the momentum of the particle.

Write the expression for the momentum of photons.

p=Ec (II)

Here, E is the energy of photon, and c is the speed of light.

From equation (II), photon with higher energy will have higher momentum. Energy of the photon in option (a) is higher than the energy of photon of option (d). From equation (I) it is clear that photon with least energy has longer wavelength. Thus d>a.

Write the expression for the relativistic energy of particle.

E2=p2c2+m2c4 (III)

Rewrite expression (III) for pc.

pc=(E2m2c4)12 (IV)

Write the expression for kinetic energy of the particle.

K=Emc2 (V)

Solve expression (V) for E.

E=K+mc2 (VI)

Use expression (VI) in (IV).

pc=([K+mc2]2m2c4)12=(K2+2Kmc2)12 (VII)

The kinetic energy of both electron and proton of options (b) and (c) are equal. Then from equation (VII), it is clear that momentum of particle is directly proportional to the mass of the particle. Mass of proton is greater than mass of electron. So the momentum of proton is greater than momentum of electron. Again from equation (I), particle with small momentum have longer wavelength. Thus b>c.

Substitute 3eVc for p in equation (II).

3eVc=EcE=3eV

Thus the energy of electron of option (e) has energy 3eV which is equal to the energy of particles of option (a). Thus the wavelength of particle of option (e) is equal to the wavelength of option (a). Thus a=e.

Thus combining all the results the ranking of the particles based on the wavelength is d>a=e>b>c_.

Conclusion:

Therefore, the ranking of the wavelengths of the quantum particles is d>a=e>b>c_.

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Chapter 40 Solutions

Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term

Ch. 40 - Prob. 4OQCh. 40 - Prob. 5OQCh. 40 - Prob. 6OQCh. 40 - Prob. 7OQCh. 40 - Prob. 8OQCh. 40 - Prob. 9OQCh. 40 - Prob. 10OQCh. 40 - Prob. 11OQCh. 40 - Prob. 12OQCh. 40 - Prob. 13OQCh. 40 - Prob. 14OQCh. 40 - Prob. 1CQCh. 40 - Prob. 2CQCh. 40 - Prob. 3CQCh. 40 - Prob. 4CQCh. 40 - Prob. 5CQCh. 40 - Prob. 6CQCh. 40 - Prob. 7CQCh. 40 - Prob. 8CQCh. 40 - Prob. 9CQCh. 40 - Prob. 10CQCh. 40 - Prob. 11CQCh. 40 - Prob. 12CQCh. 40 - Prob. 13CQCh. 40 - Prob. 14CQCh. 40 - Prob. 15CQCh. 40 - Prob. 16CQCh. 40 - Prob. 17CQCh. 40 - The temperature of an electric heating element is...Ch. 40 - Prob. 2PCh. 40 - Prob. 3PCh. 40 - Prob. 4PCh. 40 - Prob. 5PCh. 40 - Prob. 6PCh. 40 - Prob. 7PCh. 40 - Prob. 8PCh. 40 - Prob. 9PCh. 40 - Prob. 10PCh. 40 - Prob. 11PCh. 40 - Prob. 12PCh. 40 - Prob. 14PCh. 40 - Prob. 15PCh. 40 - Prob. 16PCh. 40 - Prob. 17PCh. 40 - Prob. 18PCh. 40 - Prob. 19PCh. 40 - Prob. 20PCh. 40 - Prob. 21PCh. 40 - Prob. 22PCh. 40 - Prob. 23PCh. 40 - Prob. 25PCh. 40 - Prob. 26PCh. 40 - Prob. 27PCh. 40 - Prob. 28PCh. 40 - Prob. 29PCh. 40 - Prob. 30PCh. 40 - Prob. 31PCh. 40 - Prob. 32PCh. 40 - Prob. 33PCh. 40 - Prob. 34PCh. 40 - Prob. 36PCh. 40 - Prob. 37PCh. 40 - Prob. 38PCh. 40 - Prob. 39PCh. 40 - Prob. 40PCh. 40 - Prob. 41PCh. 40 - Prob. 42PCh. 40 - Prob. 43PCh. 40 - Prob. 45PCh. 40 - Prob. 46PCh. 40 - Prob. 47PCh. 40 - Prob. 48PCh. 40 - Prob. 49PCh. 40 - Prob. 50PCh. 40 - Prob. 51PCh. 40 - Prob. 52PCh. 40 - Prob. 53PCh. 40 - Prob. 54PCh. 40 - Prob. 55PCh. 40 - Prob. 56PCh. 40 - Prob. 57PCh. 40 - Prob. 58PCh. 40 - Prob. 59PCh. 40 - Prob. 60APCh. 40 - Prob. 61APCh. 40 - Prob. 62APCh. 40 - Prob. 63APCh. 40 - Prob. 64APCh. 40 - Prob. 65APCh. 40 - Prob. 66APCh. 40 - Prob. 67APCh. 40 - Prob. 68APCh. 40 - Prob. 69APCh. 40 - Prob. 70APCh. 40 - Prob. 71APCh. 40 - Prob. 72CPCh. 40 - Prob. 73CPCh. 40 - Prob. 74CPCh. 40 - Prob. 75CPCh. 40 - Prob. 76CP
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