JEE Main 2020 · 9 January · evening · Single correct · +4 / −1
An electron of mass m and magnitude of charge |e| initially at rest gets accelerated by a constant electric field E. The rate of change of de-Broglie wavelength of this electron at time t ignoring relativistic effects is :
- (a) (- h)/(| e |Et)
- (b) (- h)/(| e |E√t)
- (c) (- h)/(| e |Et²)
- (d) (| e |Et)/h
Answer and solution
Answer (c) (- h)/(| e |Et²)
Solution
Physics sir · 3 steps
Momentum grows linearly with time, so the wavelength falls as 1/t. Now differentiate that.
- Momentum at time t. The force on the electron is |e|E, and it is constant. Starting from rest, the momentum after time t is p = |e|Et, because force is the rate of change of momentum.
- Wavelength at time t. The de Broglie relation λ = h/p gives λ = h/|e|Et. Here h, |e| and E are constants, so only t changes.
dλ/dt = h/|e|E d/dt(1/t) = -h/(|e|E t²)
- So. The wavelength shrinks at the rate -h/|e|Et². The minus sign says λ decreases as the electron speeds up. The answer is (c).
The idea to keep. For a constant force from rest, p = Ft, so λ = h/Ft. Write λ as a function of time first, then differentiate. Do not stop at λ itself.
Answer from the NTA final answer key. Solution by PrepWiser.