Electrons used in an electron microscope are accelerated by a voltage of `25 kV`. If the voltage is increased to `100 kV` then the de - Broglie wavelength associated with the electrons would

Options

A. decrease by `2` times
B. decrease by `4` times
C. increase by `4` times
D. increase by `2` times

Answer

A

Explanation

We have `lambda = (12.27)/(sqrt(V))`
So , `(lambda_(1))/(lambda_(2)) = sqrt((V_(2))/(V_(1))) rArr lambda_(2) = lambda_(1) sqrt((V_(1))/(V_(2)))`
`lambda_(2) = lambda_(1) sqrt((25)/(100)) rArr lambda_(2) = lambda_(1) sqrt((1)/(2)) = (lambda_(1))/(2)`