Question

If one were to apply Bohr's model to a particle of mass 'm' and charge 'q' moving in a plane under the influence of a magnetic field 'B', the energy of the charged particles in the $n^{th}$ level will be:

• A. n$\left(\frac{hqB}{8\pi m}\right)$
• B. n$\left(\frac{hqB}{4\pi m}\right)$
• C. n$\left(\frac{hqB}{2\pi m}\right)$
• D. n$\left(\frac{hqB}{\pi m}\right)$

Answer 1

The correct option is A n$\left(\frac{hqB}{8\pi m}\right)$

According to given data

We know that,

$mvr=\frac{nh}{2\pi }$

Or,

$qvB=\frac{m{v}^2}{r}$

So we find,

$qB=\frac{mv}{r}$

$qB\left(\frac{nh}{2\pi mv}\right)=mv$

$\left(\frac{1}{2}m{v}^2\right)=\frac{nhqB}{4\pi m}$

$E=n\left(\frac{hqB}{4\pi m}\right)$

This is the required solution.