Question

α-particle, proton & electron have same kinetic energy. Select correct order of their de-Broglie wavelength.

• A. λe > λp > λα
• B. λα > λe > λp
• C. λp = λα = λe
• D. λp > λe > λα

Answer 1

Answer: (A)

λe > λp > λα

Answer 2

The matter waves, the wavelength is associated with the microscopic particles like protons, electrons, neutrons, $\alpha$-particle etc., is or the order of $10^{-10}m$.
The relation between de-Broglie wavelength $\lambda$ and the kinetic energy $K$ of the particle is given by:
$λ = \frac{h}{m.v} = \frac{h}{√(2.m.K.E)}$
$\text{as K.E. is same } λ∝\frac{1}{\sqrt{m}}$
mass of electron = $9.1 × 10^{-31}$ kg
mass of proton = $1.67 × 10^{-27}$ kg
mass of α-particle = $6.68 × 10^{-27}$ kg
$λ_e > λ_p > λ_α$

So, the correct option is (A): $λ_e > λ_p > λ_α$