A particle is dropped from height H. The de-Broglie wavelength of the particle as a function of height is proportional to:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( H^{-1/2} \)
The de Broglie wavelength of a particle is \( \lambda = h/p = h/(mv) \). A particle dropped from rest through a height H reaches the speed given by \( v^{2} = 2gH \).
\( \displaystyle \lambda = \frac{h}{mv} = \frac{h}{m\sqrt{2gH}} \)
For a given particle h, m and g are constants, so \( \lambda\propto H^{-1/2} \).
Note: A similar question was also asked in CUET (UG) 2026 on 22-05-2026 (Slot 1), and in CUET (UG) 2023 on 13-06-2023 (Slot 3).