Question

In $YDSE$, an electron beam is used to obtain interference pattern, If speed of electron is increased then

• A. no interference pattern will be observed.
• B. distance between two consecutive fringes will increase.
• C. distance between two consecutive fringes will decrease.
• D. distance between two consecutive fringes remains same.

Answer 1

The correct option is C distance between two consecutive fringes will decrease.

We have

$\lambda =\frac{h}{mv}$

where$\lambda$ is the wavelength. $h$ is Planck's constant, $m$ is the mass and vv 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.