A particle at rest is dropped from a 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 is \( \lambda = h/p = h/mv \). A particle dropped from rest gains speed as it falls, so find v in terms of H by conservation of energy.
\( \displaystyle mgH = \frac{1}{2}mv^{2} \Rightarrow v = \sqrt{2gH} \)
\( \displaystyle \lambda = \frac{h}{m\sqrt{2gH}} \)
\( \displaystyle \lambda \propto H^{-1/2} \)
Note: A similar question was also asked in CUET (UG) 2023 on 13-06-2023 (Slot 3) and on 05-06-2023 (Slot 3).
Note: This question is from the NCERT Exemplar. NTA sets numerical questions from the Exemplar too, so do not ignore it while practising numericals.
NCERT Exemplar:
Dual Nature of Radiation and Matter – …
