Question

An electron is accelerated through a potential difference of $1000\, V$, its velocity is nearly

• A. $3.8 \times 10^{7}\, ms ^{-1}$
• B. $1.9 \times 10^{6} \, ms ^{-1}$
• C. $1.9 \times 10^{7}\, ms ^{-1}$
• D. $5.7 \times 10^{7} \, ms ^{-1}$

Answer 1

Answer: (C)

When an electron is accelerated by a potential difference of $V$ volts, then
or $e V=U$
This potential energy is converted into $KE$ of electron,
$KE=U$
$\Rightarrow \frac{1}{2} m v^{2} =e V$
$\Rightarrow v=\sqrt{\frac{2 e V}{m}}=\sqrt{\frac{2 \times 1.6 \times 10^{-19} \times 1000}{9.1 \times 10^{-31}}}$
$=1.875 \times 10^{7} $
$\approx 1.9 \times 10^{7}\, ms ^{-1}$