Question 150 of 191

A parallel beam of electrons travelling in x - direction falls on a slit of width d (see figure). If after passing the slit, an electron acquires momentum ${p}_{y}$ in the y - direction then for a majority of electrons passing through the slit (h is Planck's constant):

A$|{p}_{y}|d\lt h$B$|{p}_{y}|d\gt h$C$|{p}_{y}|d≃h$D$|{p}_{y}|d\gt \gt h$

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Answer: (A) $|{p}_{y}|d\lt h$

The electron beam will be diffractive at an angle $\theta$



For Ist minima

$d\sin ⁡\theta =\lambda$

$d\sin ⁡\theta =\dfrac{h}{p}$

Also $p\sin ⁡\theta ={p}_{y}$

$\Rightarrow d{p}_{y}=h$

$∴$ majority of electrons passing through the slit are lying in the central maxima $d{p}_{y}\lt h$