Concept explainers
(a)
The de Broglie wavelength of the electron.
(a)
Answer to Problem 87P
The de Broglie wavelength of the electron is
Explanation of Solution
The accelerating potential is
Write the expression for de Broglie wavelength
Here,
Write the expression for kinetic energy
Here,
Rearranging the above equation
Substituting (III) in (I)
Write the expression for kinetic energy in terms of accelerating potential
Here
Substituting (V) in (VI)
Substitute
Thus, the de Broglie wavelength of the electron is
(b)
Find the diffraction angle for first order maximum in Bragg’s diffraction.
(b)
Answer to Problem 87P
The Bragg angle for first order maximum is
Explanation of Solution
Write Bragg’s law to find Bragg angle
Here,
Rearranging (VII) for
Substitute
Thus, the Bragg angle is
(c)
Check whether the scattering angle is
(c)
Answer to Problem 87P
Yes. The Bragg’s scattering angle agrees with the observed scattering angle.
Explanation of Solution
The Bragg angle is
A sketch of the Bragg diffraction showing the relation between the Bragg angle and the scattering angle.
Write the phase difference between the incident beam and the scattered beam (refer figure 1)
Here,
Substituting
Write the expression for percentage error
Here,
Substituting
Since the percentage error is small, the Bragg’s scattering angle agrees with the actual scattering angle.
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