A charged particle of charge q and mass m executes a uniform circular motion in | TestHub

Passage / Comprehension

Bohr and Sommerfeld postulated the periodic motion of a particle moving in a conservative force field. They stated that the momentum $p$ and displacement $s$ are related by the following quantization rule:

$\oint p \cdot d s = nh$

Where $\oint$ denotes the integral over a single periodic closed path. For example, for an electron moving in a circular path in a hydrogen atom:

$\oint p d s = nh$

Since $p$ is constant in a circular path, $m v \times 2 π r = nh$ , which is Bohr's quantization principle for the Bohr atom. Now, we apply this condition to other periodic motions.

A charged particle of charge $q$ and mass $m$ executes a uniform circular motion in the presence of a uniform and constant magnetic field $B_{0}$ . What is the ratio of radii of circular motion of the particle in $4^{th}$ excited state to that in $2^{nd}$ excited state? Write in terms of X / 100 then find x ?

Answer:

128.00

Solution:

$mv (2 π r) = nh$ with $mv = B_{0} qr$

$\Rightarrow r \propto n^{1/2} \Rightarrow \frac{r _{5}}{r _{3}} = \frac{5}{3} \approx 1.291$

Physics - Current Electricity Question with Solution | TestHub

Doubts & Discussion

JEE Advanced (2028)