Verified Solution • 2025–26 Session moderate

QPages 384-386: Q6: HC Verma: Concepts of Physics - Volume 2 Bohr's Model and Physics of the Atom Pages 384-386: Q6 Solution: Find the radius and energy of a He ion in the states a) , b)…

⚠️ Common Exam Traps & Conceptual Pitfalls

In the Bohr model bound states have negative total energy. Students often drop the minus sign when applying $E_n=-13.6,Z^2/n^2$ eV, so remember to keep the negative sign for all bound‑state energies.

Find the radius and energy of a He+^+ ion in the states a) n=1n = 1, b) n=4n = 4 and c) n=10n = 10.

Step-by-Step Verified Solution

**Answer:** (a) n=1: r = 0.265 �, E = _54.4 eV (b) n=4: r = 4.24 �, E = _3.4 eV (c) n=10: r = 26.5 �, E = _0.544 eV. **Step-by-Step Explanation:** For He_ (Z = 2):
rn=0.529×n2Z �=0.529n22 �r_n = \frac{0.529 \times n^2}{Z} \text{ �} = \frac{0.529 n^2}{2} \text{ �}
En=−13.6×Z2n2=−13.6×4n2=−54.4n2 eVE_n = -13.6 \times \frac{Z^2}{n^2} = -13.6 \times \frac{4}{n^2} = -\frac{54.4}{n^2} \text{ eV}
(a) n=1: r = 0.265 �, E = _54.4 eV (b) n=4: r = 0.529 _ 16/2 = 4.24 �, E = _54.4/16 = _3.4 eV (c) n=10: r = 0.529 _ 100/2 = 26.5 �, E = _54.4/100 = _0.544 eV [citation:3][citation:11]

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