A particle at rest decays in to two particles of mass m₁ and m₂ and move with velocities v₁ and v₂ . The ratio of their de Broglie wave length ₁ ₂ is:

Step-by-step solution

Let the mass of the parent particle be M . Since the parent particle is at rest, the initial momentum is zero. By the law of conservation of linear momentum, the magnitudes of the momenta of the two decay products must be equal. 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, the wavelengths are ₁ = h p₁ and ₂ = h p₂ . Taking the ratio of the wavelengths: ₁ ₂ = h/p₁ h/p₂ = p₂ p₁ Since p₁ = p₂ , we have ₁ ₂ = p p = 1 . Therefor