An electron, a proton, a deuteron and an alpha particle, each having the same speed are in a region of constant magnetic field perpendicular to the direction of the velocities of the particles. The ra

Question

An electron, a proton, a deuteron and an alpha particle, each having the same speed are in a region of constant magnetic field perpendicular to the direction of the velocities of the particles. The radius of the circular orbits of these particles are respectively R e , R p , R d and R α . If follows that

TestHub · Accepted Answer

In perpendicular magnetic field magnetic force provided centripetal force.

By the relation

$q v B = \frac{m v^{2}}{r}$

$r = \frac{m v}{q B} r \propto \frac{m}{q}$

Since, $\frac{m}{q}$ ratio for deuteron and $α$ -particle is the same.

$(\frac{m}{q} = \frac{4}{2} = 2 f o r α - p a r t i c l e)$

$and (\frac{m}{q} = \frac{2}{1} = 2$ for deuteron).

Hence, the radius is the same for both.

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