dual-nature-of-radiation-and-matter Question 33
Question: Q. 2. Consider the given figure. Suppose the voltage applied to $A$ is increased. The diffracted beam will have the maximum at a value of $\theta$ that.
(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.
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Solution:
Ans. Correct option : (c)
[NCERT Exemplar] Explanation :
In Davisson-Germer experiment, the de-Broglie wavelength of diffracted beam of electrons
$$ \begin{equation*} \lambda_{d}=\frac{12.27}{\sqrt{V}} \AA \tag{i} \end{equation*} $$
$\mathrm{V}$ is the applied voltage. If there is a maxima of the diffracted electrons at an angle $\theta$, then
$$ \begin{equation*} 2 d \sin \theta=\lambda \tag{ii} \end{equation*} $$
From equation (i), as the applied voltage in this experiment increases, the wave length $\lambda_{d}$ decreases in turn $\sin \theta$ or $\theta$ decreases by relation (ii). Hence, verifies the option (c).
