Magnetic Effects & Magnetism

JEE Main level, single correct, medium

146 of 276

Question 146 of 276

A proton and an α\alpha-particle, having kinetic energies Kp{K}_{p} and Kα{K}_{\alpha }, respectively, enter into a magnetic field at right angles. The ratio of the radii of the trajectory of proton to that of α\alpha -particle is 2:12:1. The ratio of Kp:Kα{K}_{p}:{K}_{\alpha } is:

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Answer: (D) 4:14:1

r=mvqB=pqBmαmp=4r=\dfrac{mv}{qB}=\dfrac{p}{qB}\dfrac{{m}_{\alpha }}{{m}_{p}}=4
rprα=ppqpqαpα=21\dfrac{{r}_{p}}{{r}_{\alpha }}=\dfrac{{p}_{p}}{{q}_{p}}\dfrac{{q}_{\alpha }}{{p}_{\alpha }}=\dfrac{2}{1}
pppa=2qpqa=2(12)\dfrac{{p}_{p}}{{p}_{a}}=\dfrac{2{q}_{p}}{{q}_{a}}=2\left(\dfrac{1}{2}\right)
pppα=1\dfrac{{p}_{p}}{{p}_{\alpha }}=1
KpKα=pp2pαpmαmp=(1)(4)\dfrac{{K}_{p}}{{K}_{\alpha }}=\dfrac{{p}_{p}^{2}}{{p}_{\alpha }^{p}}\dfrac{{m}_{\alpha }}{{m}_{p}}=\left(1\right)\left(4\right)

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