Atoms And Nuclei Question 269
Question: If one were to apply Bohr 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 particle in the nth level will be:
Options:
A) $ n( \frac{hqB}{2\pi m} ) $
B) $ n( \frac{hqB}{8\pi m} ) $
C) $ n( \frac{hqB}{4\pi m} ) $
D) $ n( \frac{hqB}{\pi m} ) $
Show Answer
Answer:
Correct Answer: C
Solution:
-
$ qVB=\frac{mv^{2}}{r} $
and $ \frac{nh}{2\pi }=mvr $ Multiplying equation (i) and (ii),
$ \frac{qBnh}{2\pi }=m^{2}v^{2} $
Now multiplying both sides by $ \frac{1}{2m} $ ,
$ n\frac{qBh}{4\pi m}=\frac{1}{2}mv^{2}\text{ i}\text{.e}\text{. }KE=n[ \frac{qBh}{4\pi m} ] $
