A proton and an alpha particle moving with equal speeds enter normally into a uniform magnetic field. The ratio of times taken by the proton and the alpha particle to make one complete revolution in the magnetic field is
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=‌
2Ï€m
Bq
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 ( ‌
n
c
To compare the time periods of a proton ( Tp ) and an alpha particle ( Tα ), use this ratio: ‌
Tp
Tα
=‌
mp
mα
×‌
qα
qp
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: ‌
Tp
Tα
=‌
mp
4mp
×‌
2qp
qp
=‌
1
4
×2=‌
1
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