Question

The cyclotron frequencies for a deuteron and an $\alpha -$ particle are $f_d$ and $f_{\alpha }$ respectively. Then -

• A. $f_d<f_{\alpha }$
• B. $f_d>f_{\alpha }$
• C. $f_d=f_{\alpha }$
• D. $f_d=2f_{\alpha }$

Answer 1

The correct option is C $f_d=f_{\alpha }$

In cyclotron, the time period of revolution of a particle is given by,

$T=\frac{2\pi m}{Bq}$

$\therefore$ Frequency,

$f=\frac{Bq}{2\pi m}\to$ Cyclotron frequency

So,

$\frac{f_d}{f_{\alpha }}=\frac{q_d{m}_{\alpha }}{m_d{q}_{\alpha }}$

$\Rightarrow \frac{f_d}{f_{\alpha }}=\frac{e\left(4m\right)}{2m\left(2e\right)}=1$

$\Rightarrow f_d=f_{\alpha }$

Hence, option $\left(C\right)$ is the correct answer.

Why this Question? This question gives you an understanding of the concept of cyclotron frequency.