An electron initially at rest, is accelerated through a potential… - Vidyadip

MCQ

An electron initially at rest, is accelerated through a potential difference of $200 \mathrm{volt}$, so that it acquires a velocity $8.4 \times 10^6 \mathrm{~m} / \mathrm{s}$. The value of $e / m$ of electron will be

A
$2.76 \times 10^{12} \mathrm{C} / \mathrm{kg}$
✓
$1.76 \times 10^{11} \mathrm{C} / \mathrm{kg}$
C
$0.76 \times 10^{12} \mathrm{C} / \mathrm{kg}$
D
None of these

✓

Answer

Correct option: B.

$1.76 \times 10^{11} \mathrm{C} / \mathrm{kg}$

$\frac{1}{2} m v^2=e V \Rightarrow \frac{e}{m}=\frac{v^2}{2 V}=\frac{\left(8.4 \times 10^6\right)^2}{2 \times 200}=1.76 \times 10^{11} \frac{C}{\mathrm{~kg}}$.

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