A proton (mass m and charge +e) and an α-particle (mass 4m and charge +2e) are projected with the same kinetic energy at right angles to the uniform magnetic field. Which one of the following statements will be true?

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The α−particle will be bent in a circular path with a smaller radius than that for the proton.

The radius of the path of the α−particle will be greater than that of the proton.

The α−particle and the proton will be bent in a circular path with the same radius.

The α−particle and the proton will go through the field in a straight line.

answer is C.

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Detailed Solution

r=2mKqB i.e. r ∝ mqHere kinetic energy K and magnetic field B are same.∴ rprα = mp qαmα qp = mp 2qα4mα qp =1

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