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  4. A particle of mass M at rest decays into two particles of masses m1 and m2 having non-zero velocities. The ratio of the de-Broglie wavelengths of the particles (λ1/λ2) is

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Q. A particle of mass M at rest decays into two particles of
masses $ m_1 \, and \, \, m_2 $ having non-zero velocities.
The ratio of the de-Broglie wavelengths of the particles
$ \frac{\lambda_1}{\lambda_2} $ is

IIT JEEIIT JEE 1999

Solution:

From law of conservation of momentum,
$ P_1 = P_2 $ (in opposite directions)
Now de-Broglie wavelength is given by
$ \, \, \lambda = \frac{h}{p}, $ where h = Planck's constant
Since magnitude of momentum (p) of both the particles is
equal, therefore $ \lambda_1 = \lambda_2 $
or $ \lambda_1/ \lambda_2 = 1 $