A nucleus of mass M at rest splits into two parts having masses $\frac{\mathrm{M}^{\prime}}{3}$ and $\frac{2 \mathrm{M}^{\prime}}{3}$ ($\mathrm{M}^{\prime}<\mathrm{M}$). The ratio of de Broglie wavelength of two parts will be:

JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Modern Physics

A nucleus of mass M at rest splits into two parts having masses

\frac{M ^{'}}{3}

and

\frac{2 M ^{'}}{3}

(

M^{'} < M

). The ratio of de Broglie wavelength of two parts will be:

(A) $1 : 2$
(B) $2 : 1$
(C) $1 : 1$ ✓ Correct
(D) $2 : 3$

Answer: (C)

Solution

By conservation of momentum, since the nucleus was initially at rest, the two fragments must have equal and opposite momenta:

∣ P_{1} ∣ = ∣ P_{2} ∣

. The de Broglie wavelength is

λ = \frac{h}{P}

. Since both fragments have the same momentum magnitude, they have the same de Broglie wavelength. Therefore, the ratio is

1 : 1

JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Single correct option

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