A particle of mass M at rest decays into masses m₁ and m₂ with non-zero velocities. The ratio of de Broglie wavelengths ₁ and ₂ of the particles is

Step-by-step solution

The particle of mass M is initially at rest, so its initial momentum is zero. By the law of conservation of linear momentum, the final momenta of the two particles m₁ and m₂ must be equal in magnitude and opposite in direction. Let p₁ be the magnitude of the momentum of particle m₁ and p₂ be the magnitude of the momentum of particle m₂ . Then p₁ = p₂ = p . The de Broglie wavelength of a particle is given by the relation = h p , where h is Planck's constant. For the two particles, we have ₁ = h p₁ and ₂ = h p₂ . Sin