When a charged particle moves in a magnetic field, the time it takes to make one full round (the time period) is given by:
T=‌Here,
m is the mass of the particle,
q is its charge, and
B is the magnetic field. This means the time period depends on the ratio of mass to charge (
‌To compare the time periods of a proton (
Tp ) and an alpha particle (
Tα ), use this ratio:
‌=‌×‌An alpha particle has a mass four times that of a proton (
mα=4mp ) and a charge twice that of a proton (
qα=2qp ).
Plug these values in:
‌=‌×‌=‌×2=‌This shows that the time taken by a proton is half that of the alpha particle. So, the ratio of their times is
Tp:Tα=1:2