Question

a proton and alpha particles are projected normally into magnetic field with same speed. what is the ratio and radii of trajectories of proton and alpha particles
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Answer 1

Answer:

A proton and an alpha particle are separately projected in a region , where a uniform magnetic field exists. The initial velocities are perpendicular to the direction of magnetic field . If both the particles move along circles of equal radii , the ratio of momentum of proton to alpha particle( PaPp)

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Answer 2

Answer:

The ratio of radii of proton and alpha particle is 1/2.

Explanation:

When a particle of mass (m) moves in a magnetic field (B) with a uniform velocity( v) , the radius of the trajectory is given by $r=\frac{mv}{qB}$.

let us say mass of proton=$m_p$.

mass of alpha particle is =$m_{\alpha}=4m_p$

charge of proton= e

charge of alpha particle is =2e.

Since v and B is same for both, the ration of radius of proton and electron=

$\frac{r_p}{r_{\alpha}} =\frac{mv}{eB} /\frac{4mv}{2eB}=\frac{1}{2}$.

Hence the ratio of radii of proton and alpha particle is 1/2.