Physics for Scientists and Engineers with Modern Physics
Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 44, Problem 1P

(a)

To determine

The magnitude of minimum frequency.

(a)

Expert Solution
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Answer to Problem 1P

The minimum frequency is 2.27×1023Hz.

Explanation of Solution

In this case, each photon would have same energy that is the rest mass energy of the proton to conserve momentum. The kinetic energy can be neglected in this case.

Write the expression to calculate the minimum frequency.

  f=E0h

Here, f is the minimum frequency, E0 is the rest mass energy of proton and h is the Planck’s constant.

Substitute 938.3MeV for E0 and 6.626×1034Js for h in the above equation to calculate f.

  f=938.3MeV(106eV1MeV)(1.602×1019J1eV)6.626×1034Js=2.27×1023Hz

Conclusion:

Therefore, the minimum frequency is 2.27×1023Hz.

(b)

To determine

The wavelength of each photon.

(b)

Expert Solution
Check Mark

Answer to Problem 1P

The wavelength of each photon is 1.32×1015m.

Explanation of Solution

Write the expression to calculate the wavelength.

  λ=cf

Here, λ is the wavelength,

Substitute 3.00×108m/s for c and 2.27×1023Hz for f in the above equation to calculate λ.

  λ=3.00×108m/s2.27×1023Hz=1.32×1015m

Conclusion:

Therefore, the wavelength of each photon is 1.32×1015m.

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