Question

In a Young double slit experiment, the distance between the slits is 50 $\mu m$ and the distance of the screen from the slits is 5 cm. An infrared monochromatic light is mood to produce an interference pattern with fringe width 1 mm. If the light source is replaced by an electron source to produce the same fringe width then the speed of the electrons is approximately

• A. $70m/s$
• B. $700m/s$
• C. $7000m/s$
• D. $70000m/s$

Answer 1

Answer: (B)

$700m/s$

We know that :- $w=\frac{\lambda D}{d}$

Given :- $d=50\times {10}^{-6}m,$ $w=5\times {10}^{-2}m$ and $w={10}^{-3}m$

$⟹\lambda =\frac{wd}{D}=\frac{{10}^{-3}\times 50\times {10}^{-6}}{5\times {10}^{-2}}m$

$⟹\lambda ={10}^{-6}m$

For an electron to produce same fringe width, its de-Broglie wavelength should be same as $\lambda$.

Now,for electron:-

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

$⟹v=\frac{h}{m\lambda }$

$⟹v=\frac{6.63\times {10}^{-34}}{9.1\times {10}^{-31}\times {10}^{-6}}m/s$

$⟹v\approx 700m/s$

Hence, answer is option-(B).