Question

An electron alpha particle and a proton having the same kinetic energy enter on uniform magnetic field at right angle which of these has the shortest radius

Answer 1

Answer:

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Answer 2

Shortest radius is of electron and proton and alpha particle has same radius.

We know r = $\frac{mv}{qB}$    ...(i)

where m is mass of particle, v is velocity, q is charge and B is magnetic field.

Also Kinetic Energy K = $\frac{1}{2}$ m.$v^{2}$

m.v = $\sqrt[]{2Km}$      ...(ii)

Putting value of (ii) in (i)

r = $\frac{\sqrt[]{2Km} }{qB}$

Since K and B are same as its in the question that Kinetic energy is same for all and its uniform magnetic field we can replace $\frac{\sqrt{2K} }{B}$ by K' i.e a constant.

r = K'$\frac{\sqrt{m} }{q}$

Let p be notation for proton, $\alpha$ for alpha particle and e for electron

Now we know $m_{\alpha}$ = $4.m_{p}$ and $q_{\alpha}$ = 2.$q_{p}$

So $r_{\alpha}$ = $r_{p}$

i.e radius by alpha is equal to radius by proton

Since  $m_{p}$ > $m_{e}$ and  $q_{p}$ = $q_{e}$

therefore $r_{p}$ > $r_{e}$

radius by proton is greater than radius by electron