JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Modern Physics

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A particle of mass 4 M at rest disintegrates into two particles of mass M and 3 M respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass M to that of mass 3 M will be :

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

Answer: (B)

Solution

The parent is at rest, so the total momentum of the two fragments is zero and they fly apart with momenta of equal magnitude:

p_{M} = p_{3 M} = p

The de Broglie wavelength

λ = \frac{h}{p}

is fixed by the momentum alone and not by the mass, so the two fragments have the same wavelength and the ratio is

1 : 1

JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Single correct option

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