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An α-particle and a proton are projected in a uniform magnetic field in a direction perpendicular to the field. If r be the radius of circular path energy of α-particle to that of proton is

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a

1 : 4

b

2 : 1

c

4 : 1

d

1 : 2

answer is C.

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Detailed Solution

kinetic energy, K=12mv2⇒v=2Km∴r=vω=2K/mQB/m=2KmQB⇒K=Q2B2r22m⇒K∝Q2r2m ∴KαKp=QαQp2.rαrp2.mpmα2=2ee2.22.m4m=4

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