An α -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 α…

Question

An &#945; -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 &#945; -particle and the sulphur ion move in circular orbits of radii R &#945; and R S , respectively. The ratio R S R &#945; is __________ .

Aicharya · Accepted Answer

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

$∵ R = \frac{m v}{q B} = \frac{\sqrt{2 m E}}{q B} = \frac{\sqrt{2 m q V}}{q B} = \frac{\sqrt{2 m V}}{\sqrt{q} B}$

According to given data,

$∵ V = constant & B = constant$

$∴ R \propto \sqrt{\frac{m}{q}}$

$\frac{R_{α}}{R_{S}} = \sqrt{\frac{m_{α}}{q_{α}} \times \frac{q_{S}}{m_{S}}} = \sqrt{\frac{4}{2} \times \frac{1}{32}}$

$\Rightarrow \frac{R_{α}}{R_{S}} = \sqrt{\frac{1}{16}} = \frac{1}{4}$

Then, $\frac{R_{S}}{R_{α}} = 4$

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An α -particle (mass 4 amu) and a singly charged Sulphur ion (mass 32 amu) are initially at rest. They…

Solution

An &#945; -particle (mass 4 amu) and a singly charged Sulphur ion (mass 32 amu) are initially at rest. They…

Solution

An α -particle (mass 4 amu) and a singly charged Sulphur ion (mass 32 amu) are initially at rest. They…