Concept explainers
(a)
The maximum fractional energy loss for the
(a)
Answer to Problem 36P
The maximum fractional energy loss for the
Explanation of Solution
Write the Compton shift equation.
Here,
The energy of the gamma ray and its wavelength are inversely proportional. The maximum energy loss will occur for maximum increase in wavelength of the gamma ray.
The value of
Substitute
Write the equation for the fractional energy loss of the Gamma ray.
Here,
Write the equation for the energy of incident gamma ray.
Here,
Write the equation for the energy of the scattered gamma ray.
Here,
Put equations (IV) and (V) in equation (III).
Write the equation for the Compton shift in the gamma ray’s wavelength.
Rewrite equation (VII) for
Put equation (VII) in the numerator of equation (VI) and replace denominator of equation (VI) by (VIII).
Rewrite equation (IV) for
Put equations (II) and (X) in equation (IX).
Conclusion:
The value of
Substitute
Therefore, the maximum fractional energy loss for the
(b)
The maximum fractional energy loss for the
(b)
Answer to Problem 36P
The maximum fractional energy loss for the
Explanation of Solution
Equation (XI) can be used to find the fractional loss of the gamma ray when it is Compton scattered from the free proton by using the mass of the proton in the equation.
Conclusion:
The mass of proton is
Substitute
Therefore, the maximum fractional energy loss for the
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