Concept explainers
(a)
The wavelength of the neutron that undergoes strong Bragg’s diffraction.
(a)
Answer to Problem 83P
The wavelengths of the neutron are
Explanation of Solution
The speed range of the neutron is
Write the expression for de Broglie wavelength
Here,
The de Broglie wavelength is inversely proportional to velocity and hence greater velocity corresponds to smaller wavelength and vice versa.
Substitute
Thus, the minimum de Broglie wavelength of the neutron is
Substitute
Thus, the maximum de Broglie wavelength of the neutron is
Thus, the range of de Broglie wavelength lies between
Write Bragg’s law to find wavelength
Here,
Rearranging (II)
Substituting
Substituting
Substituting
Substituting
From the above calculated wavelengths, the wavelengths fitting the range of de Broglie wavelength are only the first three.
Thus, the wavelengths of the neutron that undergoes strong Bragg’s diffraction are
(b)
The angle of emergence with respect to the incident beam.
(b)
Answer to Problem 83P
The angle of emergence is
Explanation of Solution
The angle of incidence is
Angle of reflection tells that the angle of incidence and angle of reflection is same for plane surfaces.
The vertically opposite angles are equal and hence the angle of emergence with respect to the incident beam is twice the angle of incidence i.e.
Thus the angle of emergence is
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Chapter 28 Solutions
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