Explanation

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