Question

The velocity acquired by an electron at rest when subjected to a uniform electric field of potential difference $180~\text{V}$ is:
(Mass of electron $= 9 \times 10^{-31}$ kg and charge of electron $= 1.6 \times 10^{-19}$ C)

• A. $400~\text{km s}^{-1}$
• B. $4000~\text{km s}^{-1}$
• C. $800~\text{km s}^{-1}$
• D. $8000~\text{km s}^{-1}$

Hint:

Use the formula $v = \sqrt{\dfrac{2eV}{m}}$ for velocity of a charged particle accelerated from rest through a potential difference.

Answer 1

The Correct Option is D

Step 1: Use energy conservation
The work done on the electron is converted to kinetic energy:
\[ eV = \frac{1}{2}mv^2 \] Step 2: Solve for velocity $v$
\[ v = \sqrt{\frac{2eV}{m}} = \sqrt{\frac{2 \times 1.6 \times 10^{-19} \times 180}{9 \times 10^{-31}}} \] \[ v = \sqrt{\frac{5.76 \times 10^{-17}}{9 \times 10^{-31}}} = \sqrt{6.4 \times 10^{13}} \approx 8 \times 10^6~\text{m/s} = 8000~\text{km/s} \]