Question

In YDSE, an electron beam is used to obtain interference patterns. If speed of the electron is increased

• A. no interference pattern will be observed
• B. distance between the consecutive fringes will be increased
• C. distance between the two consecutive fringes will be decreased
• D. distance between the two consecutive fringes remains same

Answer 1

Answer: (C)

distance between the two consecutive fringes will be decreased

We have
$\lambda =\frac{h}{mv}$
where $\lambda$ is the wavelength. $h$ is Planck's constant, $m$ is the mass and $v$ is the velocity.
$⟹\lambda \propto \frac{1}{v}$
If the velocity of an electron increases then wavelength decreases.
Also we have fringe width,
$\beta =\frac{\lambda D}{d}$
$⟹\beta \propto \lambda$
Since wavelength decreases, fringe width will also decrease.