A nucleus A, with a finite de–Broglie wavelength λA, undergoes spontaneous fission into two nuclei B and C of equal mass. B flies in the same direction as that of A, while C flies in the opposite direction with a velocity equal to half of that of B. The de–Broglie wavelengths λB and λC of B and C are respectively

Engineering

Physics

Momentum and Energy Conservation for System of Particles

de Broglie Hypothesis and Dual Nature

Question

A nucleus A, with a finite de–Broglie wavelength λ_A, undergoes spontaneous fission into two nuclei B and C of equal mass. B flies in the same direction as that of A, while C flies in the opposite direction with a velocity equal to half of that of B. The de–Broglie wavelengths λ_B and λ_C of B and C are respectively

$λ_{A}, \frac{λ_{A}}{2}$

$\frac{λ_{A}}{2}, λ_{A}$

λ_A, 2λ_A

2λ_A, λ_A

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Let mass of B and C is m each. By momentum conservation

$2 {mv}_{0} = mv - \frac{mv}{2}$

v = 4v₀

P_A = 2mv₀ p_B = 4mv₀ p_C = 2mv₀

De-Broglie wavelength $λ = \frac{h}{p}$

$λ_{A} = \frac{h}{2 {mv}_{0}}; λ_{B} = \frac{h}{4 {mv}_{0}}; λ_{C} = \frac{h}{2 {mv}_{0}}$