The ratio of de Broglie wavelength of a deutron with kinetic energy E to that of an alpha particle with kinetic energy 2E, is n : 1. The value of n i $s ________.$
(Assume mass of proton = mass of neutron)

Question

The ratio of de Broglie wavelength of a deutron with kinetic energy E to that of an alpha particle with kinetic energy 2E, is n : 1. The value of n i $s ________.$

(Assume mass of proton = mass of neutron)

G1 Physics · Accepted Answer

The de Broglie wavelength for a non-relativistic particle is λ = h/√(2mK). Let proton and neutron mass each be m. Then deuteron mass is approximately m(d) = 2m. Alpha-particle mass is approximately m(α) = 4m. Given, K(d) = E, K(α) = 2E. Therefore, λ(d)/λ(α) = √[ m(α)K(α)/ {m(d)K(d)} ]. Hence, λ(d)/λ(α) = √[ (4m)(2E)/ {(2m)(E)} ] = √4 = 2. Therefore, n = 2.

The ratio of de Broglie wavelength of a deutron with kinetic energy E to that of an alpha particle with kinetic energy 2E, is n : 1. The value of n i s ________. (Assume mass of proton = mass of neutron)