Question

A cyclotron is used to accelerate protons, deuterons, $\alpha$-particles etc. If the energy attained, after acceleration, by the protons is $E$, the energy attained by $\alpha$-particles shall be

• A. $ 4E $
• B. $ 2E $
• C. $ E $
• D. $ E $ /4

Answer 1

Answer: (C)

For a cyclotron, maximum energy gained by the charged particle
$E_{\max }=\left[\frac{q^{2} B^{2}}{2 m}\right] r^{2}$
As $q_{\alpha}=2 q_{p} $
$m_{\alpha}=4 m_{p}$
$\left(E_{\max }\right)_{\text {proton }}=\left(E_{\max }\right)_{\text {alpha }}$