Question

In Young's double slit experiment, an electron beam is used to produce interference fringes of width β1 . Now the electron beam is replaced by a beam of protons with the same experimental set-up and same speed. The fringe width obtained is β2 . The correct relation between β1 and β2 is

• A. β₁=β₂
• B. No fringes are formed
• C. β₁<β₂
• D. β₁>β₂

Answer 1

The Correct Option is D

In Young's double slit experiment, an electron beam is used to produce interference fringes of width \( \beta_1 \). Now, the electron beam is replaced by a beam of protons with the same experimental setup and same speed. The fringe width obtained is \( \beta_2 \). The correct relation between \( \beta_1 \) and \( \beta_2 \) is:

The fringe width \( \beta \) in Young's double-slit experiment is given by the formula:

\[ \beta = \frac{\lambda D}{d} \] where:

• \( \lambda \) is the wavelength of the particle,
• \( D \) is the distance between the screen and the slits,
• \( d \) is the distance between the slits.

 

The de Broglie wavelength \( \lambda \) of a particle is given by:

\[ \lambda = \frac{h}{mv} \] where:

• \( h \) is Planck's constant,
• \( m \) is the mass of the particle,
• \( v \) is the velocity of the particle.

 

Since protons are much heavier than electrons, their de Broglie wavelength will be smaller. This results in a smaller fringe width for protons compared to electrons. Hence, we expect:

\[ \beta_1 > \beta_2 \]

Correct Answer: (D) \( \beta_1 > \beta_2 \)