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 t

Question

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 n^ th orbital will therefore be proportional to :

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Correct answer: C. n^ 1 / 2

According to the question, aligned & 2 r = n = nh p = nh mv & or mvr = nh 2 or mv = nh 2 r & F = qv _ B = mv ^2 r & or, q _ B = mv r = nh 2 r r & or, r ^2= nh 2 qB & or, r = nh 2 qB & i.e., r n ^ 1 / 2 aligned

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 n^ th orbital will therefore be proportional to :

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