If the de Broglie wavelengths associated with a proton and `alpha` particle are equal then the ration of velocites of the proton and the `alpha` paricle will be :

Options

A. `1:4`
B. `1:2`
C. `4:1`
D. `2:1`

Answer

C

Explanation

According to question , `lamda_p = lamda_alpha`
So, `(h)/(m_p xx v_p) = (h)/(m_alpha xx v_alpha) rArr v_p/v_alpha = m_alpha/m_p = (4m_p)/(m_p)`
(`because` mass of `alpha - ` particle is 4 times of mas of proton )
So, `v_p/v_alpha = 4/1 , i.e., 4:1`