An α -particle (mass 4 amu) and a singly charged Sulphur ion (mass...

When a particle moves on a circular path in a magnetic field then,

$∵ R = \dfrac{mv}{qB} = \dfrac{\sqrt{2mE}}{qB} = \dfrac{\sqrt{2mqV}}{qB} = \dfrac{\sqrt{2mV}}{\sqrt{q}B}$

According to given data,

$∵ V = \text{constant}\text{\text{ and }}B = \text{constant}$

$∴ R ∝ \sqrt{\dfrac{m}{q}}$

$\dfrac{{R}_{\alpha}}{{R}_{S}} = \sqrt{\dfrac{{m}_{\alpha}}{{q}_{\alpha}} \times \dfrac{{q}_{S}}{{m}_{S}}} = \sqrt{\dfrac{4}{2} \times \dfrac{1}{32}}$

$⇒ \dfrac{{R}_{\alpha}}{{R}_{S}} = \sqrt{\dfrac{1}{16}} = \dfrac{1}{4}$

Then, $\dfrac{{R}_{S}}{{R}_{\alpha}} = 4$