Orbits of a particle moving in a circle are such that the perimeter of the orbit equals an integer number of de-Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the nth orbital will therefore be proportional to

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n3/2

n1/2

answer is D.

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Detailed Solution

Given that 2πr=nλ ; 2πr=nhmVand BqV=mV2r ; r=mVBq mV=Bqr ; 2πr=nhBqr⇒r2∝n⇒r∝n1/2

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