If the de Broglie wavelengths for a proton and an $\alpha$-particle are equal, then the ratio of their velocities respectively will be:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $4: 1$
De Broglie wavelength, $λ=\frac{h}{P}=\frac{h}{mv}$
where,
P = Momentum of Particle
m = Mass of particle
v = velocity of particle
$λ_{proton}=\frac{h}{mv_1}$
$λ_{alpha}=\frac{h}{4mv_2}$
and,
$λ_{proton}=λ_{alpha}$ [given]
$\frac{h}{mv_1}=\frac{h}{4mv_2}$
$\frac{v_1}{v_2}=\frac{4}{1}$