Question

An electron and positron are accelerated from rest to the same kinetic energy. The ratio of their de Broglie wavelengths is

• A. \(1:2\)
• B. \(2:1\)
• C. \(1:4\)
• D. \(1:1\)

Hint:

For the same kinetic energy, the de Broglie wavelength depends only on the particle mass, which is equal for both.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
In terms of kinetic energy, the de Broglie wavelength is \(\lambda = \dfrac{h}{\sqrt{2mK}}\).

Step 2: Compare the particles
A positron is the antiparticle of the electron. It has the same mass and the same magnitude of charge, only the sign of charge differs.

Step 3: Calculation
Both have the same mass \(m\) and the same kinetic energy \(K\), so they have the same momentum and the same wavelength.

Final Answer:
The wavelengths are equal, so the ratio is 1 to 1. \[ \boxed{\text{(D) }1:1} \]