Question

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

• A. 10.2 MeV
• B. 2.55 MeV
• C. 20.4 MeV
• D. 5.1 MeV
• E. 1.5 MeV

Answer 1

Answer: (D)

KE of charged possible in a cyclotron,
$E_k=\frac{q^2{B}^2{r}^2}{2m}$
But frequency $f=\frac{qB}{2\pi m}$
$\therefore$ $E_k=\frac{{(2\pi mf)}^2{r}^2}{2m}=2{\pi }^{2}m{f}^2{r}^2$
Or $E_k=2\times {(3.14)}^2\times 1.67\times {10}^{-27}\times {(10\times {10}^6)}^2$
$\times {(0.5)}^2$
$=8.23\times {10}^{-13}J$
$\therefore E_k=\frac{8.23\times {10}^{-13}}{1.6\times {10}^{-19}}$
$=5.1\times {10}^{6}eV=5.1MeV$