Question

An electron is accelerated under a potential difference of $182$V. The maximum velocity of electron will be(Charge of electron is $1.6\times {10}^{-19}$C and its mass is $9.1\times {10}^{-31}$kg)

• A. $5.65\times {10}^{6}m/s$
• B. $4\times {10}^{6}m/s$
• C. $8\times {10}^{6}m/s$
• D. $16\times {10}^{6}m/s$

Answer 1

Answer: (C)

$8\times {10}^{6}m/s$

The potential difference provides the kinetic energy to the electron.

$\frac{1}{2}m{v}^2=eV$

Substitute the values in the equation:
$\frac{1}{2}\times 9\times {10}^{-31}\times v^2=1.6\times {10}^{-19}\times 182$

$v^2=\frac{1.6\times {10}^{-19}\times 182\times 2}{9.1\times {10}^{-31}}$

$=64\times {10}^{12}$

$v=8\times {10}^{6}m/s$.