Electrons are accelerated from rest through a potential difference and acquire a de…

PHYSICS · Multi-part · A Level · Physics · Particles and radiation · Particles and radiation

Problem

Electrons are accelerated from rest through a potential difference

V

and acquire a de Broglie wavelength

\lambda

(non-relativistic case). (i) Starting from relevant relations, derive an expression for

V

in terms of

h,\,m_{e},\,e

and

\lambda

. (ii) Using your expression, calculate the accelerating potential required to obtain electrons of wavelength

0.25\,\text{nm}

. Use

h=6.63\times10^{-34}\,\text{J s}

m_{e}=9.11\times10^{-31}\,\text{kg}

and

e=1.60\times10^{-19}\,\text{C}

. Give your answer correct to two significant figures.