Verified Solution • 2025–26 Session moderate

QPages 384-386: Q25: HC Verma: Concepts of Physics - Volume 2 Bohr's Model and Physics of the Atom Pages 384-386: Q25 Solution: Calculate the magnetic dipole moment corresponding to the…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently confuse the orbital radius $r$ with the Bohr radius constant $a_0$ or fail to convert the given radius from Angstroms ($10^{-10}$ m) to meters correctly, leading to a factor of $10^2$ or $10^4$ error in the final magnetic moment calculation.

Calculate the magnetic dipole moment corresponding to the motion of the electron in the ground state of a hydrogen atom.

Step-by-Step Verified Solution

**Answer:** Magnetic dipole moment = 9.27 _ 10___ A m_. **Step-by-Step Explanation:** For ground state, the electron's orbital motion is equivalent to a current loop. Current i = e/T = e/(2�r/v) = ev/(2�r). Magnetic moment _ = iA = (ev/(2�r)) _ �r_ = evr/2. Substituting v = 2.18 _ 10_ m/s, r = 0.53 _ 10___ m:
μ=1.6×10−19×2.18×106×0.53×10−102=9.27×10−24 A m2\mu = \frac{1.6 \times 10^{-19} \times 2.18 \times 10^6 \times 0.53 \times 10^{-10}}{2} = 9.27 \times 10^{-24} \text{ A m}^2
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