Question

Orbits of a particle moving in a circle are such that 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:

Answer 1

For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the nth orbital will be proportional to √n

Explanation :

We know that

2πr = (nh)/(mv)

=> mv = nh/2πr

Also for a charged particle moving in a circular orbit, the centrifugal force is given by,

F = mv²/r = qv

=> q = mv/r

=> qr = mv

putting the value of mv from the above equation,

qr = nh/2πr

=> 2πr²q = nh

=> r² = nh/2πq

=> r² ∝ n

=> r ∝ √n

Hence for a charged particle moving in a plane perpendicular to a magnetic field, the radius of the nth orbital will be proportional to √n

Answer 2

n to the power3/2 is the answer I think