Verified Solution • 2025–26 Session moderate

QPages 384-386: Q26: HC Verma: Concepts of Physics - Volume 2 Bohr's Model and Physics of the Atom Pages 384-386: Q26 Solution: Show that the ratio of the magnetic dipole moment to the…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often incorrectly substitute the Bohr radius $r_n$ into the magnetic moment formula without recognizing that $r$ cancels out in the ratio $mu/L$, leading them to believe the ratio depends on the principal quantum number $n$.

Show that the ratio of the magnetic dipole moment to the angular momentum l=mvrl = mvr) is a universal constant for hydrogen-like atoms and ions. Find its value.

Step-by-Step Verified Solution

**Answer:** The ratio _/L = e/(2m) = 8.8 _ 10__ C/kg. **Step-by-Step Explanation:** Magnetic moment _ = evr/2. Angular momentum L = mvr.
μL=evr/2mvr=e2m\frac{\mu}{L} = \frac{evr/2}{mvr} = \frac{e}{2m}
This is a universal constant for all hydrogen-like atoms. Value = 1.6 _ 10___ / (2 _ 9.1 _ 10___) = 8.8 _ 10__ C/kg [citation:3].

All Questions in this Chapter

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