The radius of and `alpha`-particle moving in a circle in a constant magnetic field is half of the radius of and electron moving in circular path in the same field. The de Broglie wavelength of `alpha`-particle is n times that of the electron. Find n (an integer).

Explanation

`eprop(P)/(q)` (since,`r=(P)/(Bq)`)
where `P=` momentum, Given `r_(alpha)=(1)/(2)r_e`
`(P_(alpha))/(B2e)=(1)/(2)((P_e)/(B_e))` or `P_(alpha)=P_e`
`lamdaprop(1)/(P)` (since,`lamda=(h)/(p)`)
So, `lamda_(alpha)=lamda_e` or `n=1`