The ratio of de Broglie wavelengths of a deuterium atom to that of an `alpha`- particle, when the velocity of the former is five times greater than that of the latter, is

Options

A. 4
B. 0.2
C. 2
D. 0.4

Answer

D

Explanation

Deuterium has 1 proton and 1 neutron `alpha`-particle has 2 protons and 2 neutrons.
`:.` Mass of `alpha` -particle `(m_(alpha))` is twice that of deuterium `(m_D)` i.e, `m_(alpha) = 2m_(D)`
5 = times velocity of `alpha` - particles `(v_alpha)`
i.e., `upsilon_D = 5upsilon_(alpha) " or " upsilon_(alpha) = upsilon_(D)//5`
`lambda_D = (h)/(m_D upsilon_D)` and
`lambda_(alpha) = h/(m_(alpha) upsilon_(alpha)) = h/((2m_D)((upsilon_D)/(5)))`
or `(lambda_D)/(lambda_alpha) = h/(m_D upsilon_D) xx ((2 m_D)(upsilon_D))/(5h) = 0.4`.