Question

Instead of ordinary light, an Electron beam is used in YDSE. When KE of beam is made four times, The angular separation between 2nd and 3rd dark fringe will becomes:
(A) Two times
(B) Four times
(C) $ \dfrac{1}{2} $ times
(D) Remain same

Answer 1

Hint :The double-slit experiment is a proof in contemporary physics that light and matter may exhibit properties of both conventionally defined waves and particles, as well as the essentially probabilistic nature of quantum mechanical events.

Complete Step By Step Answer:
The double-slit experiment is a proof in contemporary physics that light and matter may exhibit properties of both conventionally defined waves and particles, as well as the essentially probabilistic nature of quantum mechanical events. Thomas Young was the first to undertake this sort of experiment with light in 1801, as a demonstration of light's wave nature. Light was assumed to be made up of either waves or particles at the time. It wasn't until the advent of modern physics, nearly a century later, that it was understood that light could behave like both waves and particles. Electron-beam technology has been the foundation for a range of unique and specialised applications in semiconductor manufacturing, microelectromechanical systems, nanoelectromechanical systems, and microscopy since the mid-twentieth century. A light beam, also known as a light beam or a light beam, is a directed projection of light energy emitted by a light source. When sunlight is filtered via clouds, trees, or windows, it generates a light beam (a sunbeam).
To obtain interference in YDSE, an electron beam is employed.
If the kinetic energy is four times that of the original kinetic energy, the velocity is two times that of the original velocity.
 $ \dfrac{1}{2}m{v^2} = kE $
 $ KE{\text{ }}\alpha \;{v^2} $
Hence we obtain that
 $ \begin{gathered}
  \beta = \dfrac{{\lambda D}}{d}\quad \\
  \theta = \dfrac{\lambda }{d}\quad \\
  \theta \;\alpha \dfrac{1}{V} \\
\end{gathered} $
 $ \lambda = \dfrac{h}{{mV}}{\text{ }} $
The angular separation will becomes $ \dfrac{1}{2} $ times
Hence option B is correct.

Note :
The angle between two sightlines, or between two point objects, as seen by an observer, is known as angular distance $ \theta $ .
The concept of angular distance appears in mathematics (particularly geometry and trigonometry) as well as in all scientific sciences (e.g. astronomy and geophysics). It appears with angular velocity, angular acceleration, angular momentum, moment of inertia, and torque in classical mechanics of spinning objects.