A beam of electron is used in Young's double slits experiment. The slit width is d. When velocity of electron is increased, then :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Fringe width decreases
Electrons show wave nature, with the de Broglie wavelength
\( \displaystyle \lambda = \frac{h}{m v} \)
so they produce interference fringes in a double-slit arrangement just as light does. The fringe width is
\( \displaystyle \beta = \frac{\lambda D}{d} \)
If the velocity \( v \) increases, \( \lambda \) decreases, and with \( D \) and \( d \) unchanged, \( \beta \propto \lambda \propto 1/v \) decreases.
NCERT (2026-27):
Wave Nature of Matter – “… De Broglie proposed that the wave length λ associated with a particle of momentum p is given as
\( \displaystyle \lambda = \frac{h}{p} = \frac{h}{m v} \qquad (11.5) \)
… Clearly, from Eq. (11.5), λ is smaller for a heavier particle (large m) or more energetic particle (large v).”