The oscillating frequency of a cyclotron is 10 MHz . If the radius of its dees is 0.5 m, the kinetic energy of a proton , which is accelerated by the cyclotron is

Options

A. 10.2 MeV
B. 2.55 MeV
C. 20.4MeV
D. 5.1 MeV

Answer

D

Explanation

KE of charged possible in a cyclotron , `E_(k)=(q^(2)B^(2)r^(2))/(2m)`
But frequency `f=(qB)/(2pim)`
`thereforeE_(k)=((2pimf)^(2)r^(2))/(2m)=2pi^(2)mf^(2)r^(2)`
or `E_(k)=2xx(3.14)^(2)xx1.67xx10^(-27)xx(10xx10^(6))^(2)xx(0.5)^(2)`
`=8.23xx10^(-13)J`
`thereforeE_(k)=(823xx10^(-13))/(1.6xx10^(-19))=5.1xx10^(6)eV=5.1MeV`