A proton, a deuteron, and an alpha particle with the same kinetic energy enter a region of uniform magnetic field, moving at right angles to . The proton moves in a circle of radius . In terms of , we have to find the radii of (a) the deuteron path and (b) the alpha particle path.

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Let the mass of proton be and its charge be e,

The mass of a deuteron is,, and its charge is also e, as deuteron is an isotope of hydrogen.

The mass of an alpha particle is, 4 and its charge is 2e.

It is given that the proton, deuteron and the alpha particle have the same kinetic energy K. The speed, v, of a particle of mass, m, and kinetic energy K is determined by the relation

Therefore,

The radius of the circular orbit of a charged particle of mass, m, charge, q, velocity,, in magnetic field , perpendicular to is determined by the relation

We, therefore, find that in terms of

the radius of the deuteron orbit will be

and the radius of the alpha particle will be