chemistry : class12 Bragg’s Law : Crystalline solids : Solid State MCQ Questions and Answers
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Bragg’s Law
MCQ questions and answers.
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MCQ Questions
1. A monochromatic X-ray beam of wavelength 0.154 nm produces a first-order Bragg reflection at a diffraction angle 2θ = 30°. What is the interplanar spacing of the crystal?
A.
0.154 nm
B.
0.297 nm
C.
0.578 nm
D.
0.075 nm
Correct Answer:
0.297 nm
Explanation:
Using Bragg’s law, nλ = 2d sin θ. Here n = 1 and θ = 15°, so d = 0.154/[2 sin(15°)] ≈ 0.297 nm.
2. For X-rays of wavelength 0.200 nm, a second-order reflection is observed from crystal planes having a Bragg angle of 30°. What is the interplanar spacing?
A.
0.100 nm
B.
0.200 nm
C.
0.346 nm
D.
0.400 nm
Correct Answer:
0.200 nm
Explanation:
Bragg’s law gives d = nλ/(2 sin θ) = (2 × 0.200)/(2 × sin 30°) = 0.400/1 = 0.400 nm. Therefore, the correct option should be 0.400 nm.
3. A crystal has an interplanar spacing of 0.250 nm and is examined using X-rays of wavelength 0.180 nm. Which of the following diffraction orders is impossible?
A.
First order
B.
Second order
C.
Third order
D.
No order is impossible
Correct Answer:
Third order
Explanation:
For a Bragg reflection, nλ ≤ 2d. Thus n ≤ 2d/λ = 0.500/0.180 ≈ 2.78. Therefore, first and second orders are possible, but third order is impossible.
4. For a fixed set of crystal planes and a fixed diffraction order, two X-ray wavelengths λ1 and λ2 produce Bragg angles θ1 and θ2, respectively. If λ2 > λ1, which relationship is necessarily correct?
A.
θ2 < θ1
B.
θ2 = θ1
C.
θ2 > θ1
D.
θ2 = 2θ1
Correct Answer:
θ2 > θ1
Explanation:
From nλ = 2d sin θ, for fixed n and d, sin θ is directly proportional to λ. Hence a larger wavelength gives a larger Bragg angle, so θ2 > θ1.
5. A second-order Bragg reflection is observed at 2θ = 40° using X-rays of wavelength 0.100 nm. What is the approximate interplanar spacing?
A.
0.073 nm
B.
0.146 nm
C.
0.292 nm
D.
0.584 nm
Correct Answer:
0.292 nm
Explanation:
Here θ = 20°. Therefore, d = nλ/(2 sin θ) = (2 × 0.100)/(2 sin 20°) = 0.100/sin 20° ≈ 0.292 nm.
6. A crystal plane spacing is 0.300 nm. A first-order Bragg reflection occurs at θ = 30°. What is the wavelength of the incident X-ray?
A.
0.150 nm
B.
0.300 nm
C.
0.450 nm
D.
0.600 nm
Correct Answer:
0.300 nm
Explanation:
Using λ = 2d sin θ/n, λ = 2 × 0.300 × sin 30°/1 = 0.300 nm.
7. A first-order reflection from a set of crystal planes occurs at 2θ = 30°. At what approximate value of 2θ will the second-order reflection occur for the same wavelength and planes?
A.
30.0°
B.
45.0°
C.
62.4°
D.
75.0°
Correct Answer:
62.4°
Explanation:
For the first order, θ1 = 15°. For the second order, sin θ2 = 2 sin 15° ≈ 0.5176, giving θ2 ≈ 31.2°. Therefore, 2θ2 ≈ 62.4°.
8. A diffraction peak is recorded at 2θ = 60° using X-rays of wavelength 0.120 nm. If the peak corresponds to the third order, what is the interplanar spacing?
A.
0.104 nm
B.
0.180 nm
C.
0.208 nm
D.
0.360 nm
Correct Answer:
0.208 nm
Explanation:
The Bragg angle is θ = 30°. Thus d = nλ/(2 sin θ) = (3 × 0.120)/(2 × 0.5) = 0.360/1 = 0.360 nm. Therefore, the correct option should be 0.360 nm.
9. For a crystal with interplanar spacing 0.250 nm irradiated with X-rays of wavelength 0.100 nm, what is the maximum possible diffraction order and its corresponding Bragg angle?
A.
Second order at 23.6°
B.
Third order at 36.9°
C.
Fifth order at 90.0°
D.
Fourth order at 53.1°
Correct Answer:
Fifth order at 90.0°
Explanation:
The condition nλ ≤ 2d gives n ≤ 0.500/0.100 = 5. Thus the maximum order is n = 5. Bragg’s law gives sin θ = 5 × 0.100/(2 × 0.250) = 1, so θ = 90°.
10. A crystal gives a first-order Bragg peak at θ = 20° with X-rays of wavelength 0.140 nm. What wavelength would produce a second-order peak at the same Bragg angle from the same planes?
A.
0.035 nm
B.
0.070 nm
C.
0.140 nm
D.
0.280 nm
Correct Answer:
0.070 nm
Explanation:
For the first peak, λ1 = 2d sin θ. For the second-order peak at the same θ, 2λ2 = 2d sin θ = λ1. Hence λ2 = λ1/2 = 0.070 nm.
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