Question

A proton, a neutron, an electron and an α-particle have same energy. If λ p , λ n , λ e and λα are the de Broglie’s wavelengths of proton, neutron, electron and α particle respectively, then choose the correct relation from the following:

• A. λ p = λ n > λ e > λα
• B. λα < λ n < λ p < λ e
• C. λ e < λ p = λ n > λα
• D. λ e = λ p = λ n = λα

Answer 1

Answer: (A)

λ p = λ n > λ e > λα

Answer 2

The correct option is(B): λα < λ n < λ p < λ e.

de Broglie wavelength

$λ=\frac{h}{p}$

$⇒λ=\frac{h}{\sqrt{2mK}}$

Where K : kinetic energy

⇒ For some K ,

$λ∝\frac{1}{\sqrt{m}}$

Since m α > m n > m p > m e

⇒ λα < λ n < λ p < λ e