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Question: Answered & Verified by Expert
Consider figure given below. Suppose the voltage applied to $\mathrm{A}$ is increased. The diffracted beam will have the maximum at value of $\theta$ that

PhysicsDual Nature of Matter
Options:
  • A
    will be larger than the earlier value
  • B
    will be the same as the earlier value
  • C
    will be less than the earlier value
  • D
    will depend on the target
Solution:
2475 Upvotes Verified Answer
The correct answer is:
will be less than the earlier value
We know that,
In Davisson - Germer experiment, the de-Broglie wavelength associated with electron is
$$
\lambda_{\mathrm{d}}=\frac{12.27}{\sqrt{\mathrm{V}}} Å
$$
where $V$ is the applied voltage. If there is a maxima of the diffracted electrons at an angle $\theta$, than
$2 d \sin \theta=\lambda$
..(ii)
From equation (i) if $\mathrm{V}$ is inversely proportional to the wavelength $\lambda_{\mathrm{d}}$, then the applied voltage $\mathrm{V}$ will increase with the decrease in the wavelengh $\lambda_{\mathrm{d}}$.
From equation (ii) if wavelength $\lambda_{\mathrm{d}}$ is directly proportional to $\sin \theta$ and hence $\theta$.
So, with the decrease in $\lambda_{\mathrm{d}} \sin \theta, \theta$ will also decrease. Hence, when the voltage applied to $\mathrm{A}$ is increased. The diffracted beam will have the maximum at a value of $\theta$ that will be less than the earlier value.

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