Question

A beam of monoenergetic electrons, which have been accelerated from rest by a potential $U$, is used to form an interference pattern in a Youngs Double Slit experiment. The electrons are now accelerated by potential $4U$. Then the fringe width.

• A. Remains the same
• B. Is half the original fringe width
• C. Is twice the original fringe width
• D. Is one-fourth the original fringe width

Answer 1

Answer: (B)

Is half the original fringe width

$eV=\frac{1}{2}m{v}^2$ so, $eV=\frac{p^2}{2m}$
and
$\lambda =\frac{h}{p},\Rightarrow V\propto \frac{1}{{\lambda }^2}$ and $\beta =\frac{n\lambda D}{d}$
So as potential $U$ becomes $4U$ then $\beta$ becomes half.