Question

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii $r_e,r_p,r_{\alpha }$ respectively in a uniform magnetic field $B.$ The relation between $r_e,r_p,r_{\alpha }$ is:

• A. $r_e>r_p=r_{\alpha }$
• B. $r_e<r_p=r_{\alpha }$
• C. $r_e<r_p<r_{\alpha }$
• D. $r_e<r_{\alpha }<r_p$

Answer 1

The correct option is B $r_e<r_p=r_{\alpha }$

$\begin{array}{c}\begin{array}{c}R=\frac{mv}{Bq}\end{array}\\ \text{Given :}{m}_e{v}_e^2=m_p{v}_p^2=m_{\alpha }{v}_{\alpha }^2\end{array}$

$\begin{array}{c}\left|q_e\right|=1,\left|q_p\right|=1,\left|q_{\alpha }\right|=2\\ \sqrt{4mp}=m_{\alpha }\end{array}$

$(r_e<r_p=r_{\alpha })$