A nucleus A, with a finite de-broglie wavelength λ A, undergoes… | JEE Main 2019 (8 Apr, Shift 2)

Q125JEE Main 2019 · 8 APR · SHIFT 2Difficult

Matter Waves: de Broglie Wavelength

A nucleus A, with a finite de-broglie wavelength $\lambda$ 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 $\lambda$ B and $\lambda$ C of B and C are respectively:

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Answer: (d)

Let A have mass $M$ , speed $v$ ; B and C have mass $M/2$ , velocities $v_B$ and $-v_B/2$ .
Momentum: $Mv = \dfrac{M}{2}v_B - \dfrac{M}{2}\cdot\dfrac{v_B}{2} = \dfrac{M}{4}v_B \Rightarrow v_B = 4v$
$p_B = 2Mv = 2p_A \Rightarrow \lambda_B = \dfrac{\lambda_A}{2}$ ; $p_C = \dfrac{M}{2}(2v) = Mv \Rightarrow \lambda_C = \lambda_A$
So the answer is (d).

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Matter Waves: de Broglie Wavelength question from JEE Main 2019 (8 Apr, Shift 2)

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