The screened nuclear charge of neutral Helium atom is given as 1.7e, where e is
the magnitude of the electronic charge. Assuming the Bohr model of the atom for
which the energy levels are En = -
Z2
2
1
n2 atomic units (Z is the atomic number),
the first ionization potential of Helium in atomic units is
Options:
(A) 0.89
(B) 1.78
(C) 0.94
(D) 3.16
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2025 Q.36)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Atomic & Molecular Physics** within *Section 6: Atomic and Molecular Physics* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Atomic & Molecular Physics:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
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