Question

In a double slit experiment using wave of certain wavelength the fringes are obtained , The fringe width is-X to obtained the fringes of same width using electrons of mass $m$ the speed of electrons should be

• A. $\frac{-hD}{Xmd}$
• B. $\frac{D}{mdX}$
• C. $\frac{dX}{mD}$
• D. $\frac{hd}{XmD}$

Answer 1

The correct option is D $\frac{hd}{XmD}$

since, we know that, in double slit experiment the fringe width $\left(\beta \right)$ is given by

$\beta =\frac{\lambda D}{d}$

$\Rightarrow x=\frac{\lambda D}{d}$

$\Rightarrow \lambda =\frac{xd}{D}$ ……(i)

According to de-Broglie hypothesis

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

$\Rightarrow \lambda =\frac{h}{p}$ ......(ii)

Where, $h\to$ Planck's constant

$p\to$ momentum of particle

from (i) and (ii)

$\frac{h}{p}=\frac{xd}{D}$

$\Rightarrow p=\frac{hD}{xd}$

Now, if velocity of electron is '$v$'

so,

$p=mv=\frac{hD}{xd}$

$\Rightarrow v=\frac{hD}{xmd}$.