# A proton, a deuteron and an alpha particle, are accelerated through the same potential difference and then subjected to a uniform magnetic field  , perpendicular to the direction of their motions. Compare (i) their kinetic energies, and (ii) if the radius of the circular path described by proton is 5 cm, determine the radii of the paths described by deuteron and alpha particle.

(i) We know that,

Kinetic energy (K.E

The kinetic energy of the proton is given as

and kinetic energy of deuteron is given as

and kinetic energy of  - particle is given as

Hence,

therefore,

(iii) We know that,

Or

where, q = charge                    ,    v=velocity

B = magnetic field         ,    m=mass

So, of compairing both forces, we get

Such that, given ; r = 5cm,

So,

If the mass of a proton is m then the mass of deuteron is 2m and the mass of alpha particle is 4m

Hence,

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