TS EAMCET · Physics · Atomic Physics
In the Bohr model an electron of mass \(m\) moves in a circular orbit around the proton. Considering the orbiting electron to be a circular current loop, the magnetic moment of the hydrogen atom, when the electron is in \(n\)th excited state. (Assume, \(h=\) Planck's constant)
- A \(\left(\frac{e}{2 m} \frac{n^2 h}{2 \pi}\right)\)
- B \(\left(\frac{e}{m}\right) \frac{n h}{2 \pi}\)
- C \(\left(\frac{e}{2 m}\right) \frac{n h}{2 \pi}\)
- D \(\left(\frac{e}{m}\right) \frac{n^2 h}{2 \pi}\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{e}{2 m}\right) \frac{n h}{2 \pi}\)
Step-by-step Solution
Detailed explanation
If \(R\) be the radius of circular path, then magnetic moment, \(M=i \times A=(e \times f) \times\left(\pi R^2\right) \quad\left(\because i=\frac{e}{T}=e f\right)\) \(=e \times\left(\frac{v}{2 \pi R}\right) \times\left(\pi R^2\right)\)…
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