JEE Advance - Physics (2021 - Paper 1 Online - No. 17)
An $$\alpha$$-particle (mass 4 amu) and a singly charged sulphur 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 rs, respectively. The ratio (rs/r$$\alpha$$) is __________.
Answer
4
Explanation
$${r_\alpha } = {{\sqrt {2{m_\alpha }{q_\alpha }V} } \over {{q_\alpha }B}}$$
$${r_s} = {{\sqrt {2{m_s}{q_s}V} }\over {{q_s}B}}$$
$${{{r_s}} \over {{r_\alpha }}} = \sqrt {{{{m_s}} \over {{q_s}}}{{{q_\alpha }} \over {{m_\alpha }}}} = \sqrt {\left( {{{32} \over 1}} \right)\left( {{2 \over 4}} \right)} $$
$${{{r_s}} \over {{r_\alpha }}} = 4$$
$${r_s} = {{\sqrt {2{m_s}{q_s}V} }\over {{q_s}B}}$$
$${{{r_s}} \over {{r_\alpha }}} = \sqrt {{{{m_s}} \over {{q_s}}}{{{q_\alpha }} \over {{m_\alpha }}}} = \sqrt {\left( {{{32} \over 1}} \right)\left( {{2 \over 4}} \right)} $$
$${{{r_s}} \over {{r_\alpha }}} = 4$$
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