Wave property of electrons implies that they will show diffractio… - Vidyadip

MCQ

Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure).

Electrons accelerated by potential $V$ are diffracted from a crystal. If $d =1\; \mathring A$, and $i =30^{\circ}$. $V$ should be about ....... $V$

$\left( h =6.6 \times 10^{-34}\; J-s , m =9.1\times 10^{-31}\; kg , e =1.610^{-19} \;C \right)$

A
$500$
✓
$50$
C
$1000$
D
$2000$

✓

Answer

Correct option: B.

$50$

b
We have,

$2 d \sin \theta= n \lambda$

angle of incidence $=90- i$

Also $n=1$ for $1^{\text {st }}$ order diffraction.

Therefore,

$2 \times 1 \times 10^{-10} \sin (90-30)=1 \times \lambda$

$\Rightarrow \lambda=2 \times 10^{-10} \frac{\sqrt{3}}{2}=\sqrt{3} \times 10^{-10} m$

We have de-Broglie wavelength, $\lambda=\frac{ h }{ mv }$

and also $\frac{1}{2} mv ^{2}= eV \Rightarrow v =\sqrt{\frac{2 eV }{ m }}$

Substituting in de-Broglie wavength, we get,

$\lambda=\frac{ h }{\sqrt{2 meV }}=\sqrt{3} \times 10^{-10} m$

$V=49.86\;V$

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