physics : class12 Compton Wavelength Shift : Particle Nature of Light : Dual Nature of Matter and Radiation MCQ Questions and Answers
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Compton Wavelength Shift
MCQ questions and answers.
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MCQ Questions
1. An X-ray photon is scattered by a free electron through an angle of 60°. What is the Compton wavelength shift? Take h/(mₑc) = 2.426 pm.
A.
0.607 pm
B.
1.213 pm
C.
2.426 pm
D.
4.852 pm
Correct Answer:
1.213 pm
Explanation:
The Compton shift is Δλ = h/(mₑc)(1 − cos θ). For θ = 60°, Δλ = 2.426(1 − 0.5) pm = 1.213 pm.
2. For Compton scattering from a free electron, the wavelength shift is maximum when the photon is scattered through which angle?
A.
0°
B.
45°
C.
90°
D.
180°
Correct Answer:
180°
Explanation:
Since Δλ = h/(mₑc)(1 − cos θ), the shift is maximum when cos θ = −1, which occurs at θ = 180°. The maximum shift is 2h/(mₑc).
3. A photon undergoes Compton scattering through 90°. If the incident wavelength is 0.100 nm, what is the wavelength of the scattered photon? Take h/(mₑc) = 0.002426 nm.
4. Two photons of different initial wavelengths undergo Compton scattering from free electrons through the same angle. Which statement about their wavelength shifts is correct?
A.
The photon with the shorter initial wavelength has the larger shift
B.
The photon with the longer initial wavelength has the larger shift
C.
Both photons have the same wavelength shift
D.
The shift depends on the intensities of the two photons
Correct Answer:
Both photons have the same wavelength shift
Explanation:
The Compton wavelength shift Δλ = h/(mₑc)(1 − cos θ) depends only on the scattering angle and the electron mass, not on the incident wavelength or intensity.
5. An X-ray beam is scattered by electrons through 60° and 120° in two separate experiments. What is the ratio of the corresponding wavelength shifts Δλ₁₂₀/Δλ₆₀?
A.
1/3
B.
1
C.
2
D.
3
Correct Answer:
3
Explanation:
The shifts are proportional to 1 − cos θ. Thus, Δλ₁₂₀/Δλ₆₀ = [1 − cos 120°]/[1 − cos 60°] = (1 + 0.5)/(1 − 0.5) = 3.
6. A photon is scattered by a free electron with a wavelength increase equal to the electron Compton wavelength h/(mₑc). What is the scattering angle?
A.
30°
B.
60°
C.
90°
D.
120°
Correct Answer:
90°
Explanation:
Setting Δλ = h/(mₑc) in Δλ = h/(mₑc)(1 − cos θ) gives 1 − cos θ = 1, so cos θ = 0 and θ = 90°.
7. For a photon scattered backward by a free electron, the wavelength shift is 4.852 pm. If the electron is replaced by a particle of mass 2mₑ, what would be the backward-scattering shift?
A.
1.213 pm
B.
2.426 pm
C.
4.852 pm
D.
9.704 pm
Correct Answer:
2.426 pm
Explanation:
For backward scattering, Δλ = 2h/(mc). Doubling the scatterer mass halves the shift. Therefore, the new shift is 4.852/2 = 2.426 pm.
8. A photon is Compton-scattered through 120° by an electron. What fraction of the maximum possible Compton wavelength shift occurs in this scattering?
A.
25%
B.
50%
C.
75%
D.
100%
Correct Answer:
75%
Explanation:
The maximum shift is obtained at 180°. The fraction is [1 − cos 120°]/[1 − cos 180°] = 1.5/2 = 0.75, or 75%.
9. An incident photon of wavelength λ is Compton-scattered through an angle θ. Which expression gives the ratio of the scattered photon energy to its incident energy?
A.
λ/[λ + h(1 − cos θ)/(mₑc)]
B.
λ/[λ − h(1 − cos θ)/(mₑc)]
C.
[λ + h(1 − cos θ)/(mₑc)]/λ
D.
1 − h(1 − cos θ)/(mₑcλ)
Correct Answer:
λ/[λ + h(1 − cos θ)/(mₑc)]
Explanation:
Since photon energy is inversely proportional to wavelength, E′/E = λ/λ′. Using λ′ = λ + h(1 − cos θ)/(mₑc) gives the stated expression.
10. In Compton scattering, the wavelength shift is measured to be 3.639 pm. Taking h/(mₑc) = 2.426 pm, determine the scattering angle.
A.
90°
B.
120°
C.
150°
D.
180°
Correct Answer:
120°
Explanation:
Using Δλ = 2.426(1 − cos θ) pm, 3.639/2.426 = 1.5 = 1 − cos θ. Hence cos θ = −0.5, giving θ = 120°.
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