Question

Calculate the speed of an electron that has fallen through a potential difference of

(a) 125 volts and

(b) 125 megavolts.

Answer 1

Explanation:

We need to find the speed of an electron that has fallen through a potential difference of  125 volts. It can be calculated using the De-broglie hypothesis as :

(a) V = 125 volts

$\dfrac{1}{2}mv^2=qV$

Where

v = speed of electron

V is potential difference

$v=\sqrt{\dfrac{2qV}{m}}$

$v=\sqrt{\dfrac{2\times 1.6\times 10^{-19}\times 125\ V}{9.1\times 10^{-31}}}$

v = 6629935.44 m/s

$v=6.62\times 10^6\ m/s$

(b) V = 125 megavolts

$V=1.25\times 10^8\ V$

$v=\sqrt{\dfrac{2qV}{m}}$

$v=\sqrt{\dfrac{2\times 1.6\times 10^{-19}\times 1.25\times 10^8\ V}{9.1\times 10^{-31}}}$

$v=6.62\times 10^9\ m/s$

Hence, this is the required solution.