Question

An electron, an $\alpha$-particle and a proton have the same kinetic energy. which of these has the longest de Broglie wavelength?

• A. a-particle
• B. proton
• C. electron
• D. both a-particle and proton

Answer 1

Answer: (C)

electron

Answer 2

The correct answer is option (C): electron
For a particle, de-Broglie wave length,
$\lambda=\frac{h}{p}$
Kinetic energy,
$K=\frac{p^2}{2m}$
Then, $\lambda=\frac{h}{\sqrt2 mk}\propto \frac{1}{m}$
so, Since an electron has the smallest mass, it also has the greatest de-Broglie wavelength.