Question

Imagine a Young’s double slit interference experiment performed with electron waves associated with fast moving electrons coming from the electron gun. The distance between successive maximum will decrease if the:
A) The accelerating voltage in the electron gun is decreased
B) The accelerating voltage is increased
C) The distance of screen from slits is increased
D) The distance between slits is increased.

Answer 1

Hint:In its current version of Young's experiment, the laser illuminates two parallel splits similarly on a non-opaque surface, which differ fundamentally only from that of a light source.

Step by Step Solution:
The ratio of the wavelength of the light to slits is an important parameter in the double-slit geometry. If $\dfrac {\lambda} {d} $ is much less than $1$, there is a slight gap between consecutive interference fringes and the interference effects cannot be visible. Young could break the disturbance ranges with closely spaced slits. He thereby defined the wavelengths of the visible light colours. Visible light's relatively short wavelength is why interference effects are detected only in specific conditions – the spacing between sources of intervening light waves must be very close to distinguish positive and disruptive interference areas.

In Young's double slit experiment with light of wavelength $\lambda $, fringe width is given by:


$\beta = \dfrac{{\lambda D}} {d} $
Where $\beta $is fringe width, $D$ is screen distance and $d$ is the slit separation

Also,
In the case of electron waves
$\lambda = \dfrac{h}{{\sqrt {2Vem}}} $


Hence, $\beta $ decreases if:
-Distance between the slits increase
-Distance of screen from the slit is decreased
-Wavelength decrease i.e. accelerating voltage increases

Note:Two other challenges render observing interference results a problem. Many light sources contain a consistent spectrum of wavelengths, resulting in certain interference patterns interacting with a particular range of margins. The various interference patterns remove the most pronounced interference results such as the dark areas. The two light sources ought to be consistent, in order for an interference pattern to be detected over some sustained period of time. This means that the light sources have a continuous phase interaction to establish.