QB_PH_SEC6_001: Atomic Spectra & Multi-Electron Atoms

In the hydrogen atom spectrum, the Lamb shift demonstrates the energy splitting between which pair of states?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Theoretical Context**: Dirac relativistic theory predicts that hydrogen atom energy levels depend strictly on principal quantum number $n$ and total angular momentum quantum number $j = l \pm 1/2$. 2. **State Evaluation**: Both $2s_{1/2}$ ($l=0, j=1/2$) and $2p_{1/2}$ ($l=1, j=1/2$) possess $n=2$ and $j=1/2$, yielding identical Dirac energies. 3. **QED Interaction**: Quantum electrodynamic vacuum fluctuations cause the electron to experience an effective smeared Coulomb potential, shifting the $s_{1/2}$ level upward relative to $p_{1/2}$ by $\approx 1057\text{ MHz}$. 4. **Conclusion**: Hence, the Lamb shift splits $2s_{1/2}$ and $2p_{1/2}$. Option (A) is correct.