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Physics Guru is an online education and competitive examinations preparation portal founded by Manish Verma, an IIT Madras alumnus, providing learning resources for competitive examinations.

The emphasis is on conceptual understanding, analytical thinking and problem solving rather than simply memorising formulas and standard methods.

The objective is to help students understand what they are learning and develop the ability to solve problems they have not seen before.

An $\alpha$-particle (mass 4 amu) and a singly ....

An $\alpha$-particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of uniform magnetic field which is normal to the velocities of the particles. Within this region, the $\alpha$-particle and the sulfur ion move in circular orbits of radii $r_{\alpha}$ and $r_S$, respectively. The ratio ($r_S/r_\alpha$) is _____.

Solution

$r = \sqrt {\frac{{2mV}}{{q{B^2}}}} $

So, $r \propto \sqrt {\frac{m}{q}} $

$\frac{{{r_S}}}{{{r_\alpha }}} = \sqrt {\frac{{{m_S}}}{{{q_S}}} \times \frac{{{q_\alpha }}}{{{m_\alpha }}}}  = \sqrt {\frac{{{m_S}}}{{{m_\alpha }}} \times \frac{{{q_\alpha }}}{{{q_S}}}}  = \sqrt {\frac{{32}}{4} \times \frac{2}{1}}  = 4$