Step-by-Step Reasoning Framework

Step 1: Identify the Species

• Is it H, $He^{+}$, $Li^{2+}$ (hydrogen-like)? → Use Bohr model formulas directly with Z
• Is it a multi-electron atom? → Use quantum numbers and electron configuration
• Is it an ion? → Determine electron count: add electrons for anions, remove for cations

Step 2: Identify the Property Asked

• Energy → Use E_n = −13.6$Z^{2}$/$n^{2}$ eV
• Wavelength/frequency → Use Rydberg: 1/λ = R_H $Z^{2}$(1/n_{1}^{2} − 1/n_{2}^{2})
• Radius → Use r_n = 0.529$n^{2}$/Z Å
• Velocity → Use v_n = $2.18 \times 10^{6}$ Z/n m/s
• Spectral lines → Use n(n−1)/2
• Nodes → Use total=n−1, angular=l, radial=n−l−1
• Quantum numbers → Check l<n, |mₗ|≤l, mₛ=±½

Step 3: Check for Traps

• Is it above or below threshold? (photoelectric)
• Is it Cr or Cu? (anomalous config)
• Is the question about which series? (Lyman=1, Balmer=2, Paschen=3)
• Is l < n satisfied? (quantum number validity)
• Is 4s removed first? (transition metal cations)

Step 4: Calculate with Units

• Always carry units through calculation
• Convert eV ↔ J using 1 eV = $1.6 \times 10^{-19}$ J
• Convert nm ↔ m using 1 nm = 10^{-9} m
• Use hc = 1240 eV·nm as shortcut

Step 5: Sanity Check

• Energy in Bohr model: always negative? ✓
• Wavelength positive? ✓
• KE of photoelectron positive? (if negative, below threshold → no emission) ✓
• Quantum numbers all in valid range? ✓