Question

An electron is accelerated from rest through a potential difference V. it's final speed is proportional to? ​

Answer 1

Given:

An electron is accelerated from rest through a potential difference $V$

To find:

The proportional value of the electron's final speed

Explanation:

According to the work-energy theorem, work done is equal to the change in kinetic energy.

$W = K_{f} - K_{i}$

$W = \frac{1}{2} mv^{2} - \frac{1}{2} mu^{2}$

Here, $u = 0$, which is at rest

Therefore, $W = \frac{1}{2} mv^{2}$

We know that, $\frac{1}{2} mv^{2}$ = $eV_{0}$

⇒ $v^{2}$ = $\frac{2eV_{0} }{m}$

⇒ $v = \sqrt{\frac{2eV_{0} }{m} }$

Answer:

Therefore, the electron's final speed ($v$) is proportional to $\sqrt{\frac{2eV_{0} }{m} }$