Question

# The ratio of the de Broglie wavelengths of a proton and an α-particle will be 1 : 2 if their:velocities are in the ratio 1 : 8velocities are in the ratio 8 : 1kinetic energies are in the ratio 1 : 64kinetic energies are in the ratio 1 : 256

Solution

## The correct option is B velocities are in the ratio 8 : 1de Broglie equation is: λ = hmv where m is the mass and v is the velocity λpλα = mαvαmpvp        eq.→1  Here, λp = wavelength of the proton λα = wavelength of the alpha particle mp = mass of the proton mα = mass of the alpha particle vp = velocity of the proton vα = velocity of the alpha particle We know, mα = 4mp  given λpλα=12 Substituting the value of mα in eq. 1, we get: λpλα = (4mp)vαmpvp 12 = 4×vαvp vpvα=81

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