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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

Asked in JEE Main 8th April 2nd Shift 2019 · Splitting and decay

Answer: (4) (λ_A)/2, λ_A

Step-by-step solution

Let A have mass M and velocity v_A; each fragment has mass M/2, with v_C=-(v_B)/2.

Momentum: /M2v_B-/M2·(v_B)/2=Mv_A, so /M4v_B=Mv_A and v_B=4v_A.

p_B=/M2·4v_A=2Mv_A=2p_A, so λ_B=(λ_A)/2.

p_C=/M2·2v_A=Mv_A=p_A, so λ_C=λ_A.

Why the other options are wrong

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