Q197 / 200 · MHT CET - Medical 2026 (26 April Shift 1) · Physics
An electron of mass m and charge e initially at rest gets accelerated by a constant electric field E. The de-Broglie wavelength of the electron at time t is (h = Planck's constant)
- Correct answerA$\dfrac{h}{eEt}$
- B$\dfrac{eEt}{h}$
- C$\dfrac{eE}{ht}$
- D$\dfrac{ht}{eE}$
Solution
The force acting on the electron in a constant electric field is $F = eE$
Since the electron is initially at rest, its momentum at time $t$ is $p = Ft = eEt$
The de-Broglie wavelength is given by $\lambda = \dfrac{h}{p}$
Substituting the value of momentum, we get $\lambda = \dfrac{h}{eEt}$
Answer: $\dfrac{h}{eEt}$
Since the electron is initially at rest, its momentum at time $t$ is $p = Ft = eEt$
The de-Broglie wavelength is given by $\lambda = \dfrac{h}{p}$
Substituting the value of momentum, we get $\lambda = \dfrac{h}{eEt}$
Answer: $\dfrac{h}{eEt}$
Hence, the correct answer is option: 'A'.