Question

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)

• A. \(\frac{h}{eEt}\)
• B. \(\frac{eEt}{h}\)
• C. \(\frac{eE}{ht}\)
• D. \(\frac{ht}{eE}\)

Hint:

Find the momentum from force times time, then use the de Broglie relation.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
The de Broglie wavelength is \(\lambda=\dfrac{h}{p}\), so we need the momentum of the electron at time \(t\).

Step 2: Momentum at Time t
The force on the electron is \(F=eE\). Starting from rest, impulse equals the change in momentum, so \(p=Ft=eEt\).

Step 3: Calculation
\(\lambda=\dfrac{h}{p}=\dfrac{h}{eEt}\).

Final Answer:
The de Broglie wavelength at time \(t\) is \(\dfrac{h}{eEt}\). \[ \boxed{\text{(A) }\dfrac{h}{eEt}} \]