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Question

Two ions of masses 4 amu and 16 amu have charges +2e and +3e respectively. These ions pass through the region of constant magnetic field perpendicular to their motion. The kinetic energy of both ions is the same. Then:

A
lighter ion will be deflected less than heavier ion
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B
no ion will be deflected
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C
lighter ion will be deflected more than heavier ion
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D
both ions will be deflected equally
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Solution

The correct option is C lighter ion will be deflected more than heavier ion
The radius of circle in which a ions will rotate inside a magnetic field is given by :
mv2r=qvB
r=mvqB=PqB
We know that :
P=2mK.E.

r=2mK.E.qB
From the above expression we can say that :
rmq
r1r2=42×316
r1r2=34
Or, r2>r1
The bigger the radius of the circular path, the smaller will be the deflection of the ion. Hence, the lighter ion will be deflected more than the heavier ion.

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