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A praticle of mass M at rest decays into...

A praticle of mass M at rest decays into two particle of masses `m_1` and `m_2`, having non-zero velocities. The ratio of the de Broglie wavelength of the particles `(lamda_1)/(lamda_2)` is

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The cracker has zero momentum before explosion. By the principle of conservation of momentum, after the explosions,
`vecp_(1) + vecp_(2) = vec0`
`therefore vecp_(1) = -vecp_(2)`
`therefore |vecp_(1)|=|vecp_(2)|`
De Broglie wavelength, `lambda = h/p`
`therefore lambda_(1)=h/p_(1)` and `lambda_(2)=h/p_(2)`
But, `p_(1)=p_(2) therefore lambda_(1)=lambda_(2) therefore lambda_(1)/lambda_(2)=1`
which gives the required ratio.
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