COMEDK · Physics · 28. Atomic Physics
What is the kinetic energy of the electron in the nth level, moving in a plane under the influence of a magnetic field 'B'? [ m-mass of electron; h- Planck's constant; e- electronic charge]
- A \(\dfrac{n h e B}{2 \pi m}\)
- B \(\dfrac{h e B}{2 \pi n m}\)
- C \(\dfrac{h e B}{4 \pi n m}\)
- D \(\dfrac{n h e B}{4 \pi m}\)
Answer & Solution
Correct Answer
(D) \(\dfrac{n h e B}{4 \pi m}\)
Step-by-step Solution
Detailed explanation
The electron moves in a circular orbit under the influence of a magnetic field \(B\). The magnetic force provides the necessary centripetal force for circular motion: \(evB = \dfrac{mv^2}{r}\) This simplifies to \(evB = \dfrac{mv^2}{r} \Rightarrow r = \dfrac{mv}{eB}\) According…
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