type: reasoning_chain | subtopic: Problem-Solving Strategy

Chain for Spectral Line Problems:

1. Identify n_{1} and n_{2} from the problem (initial and final states, or series name).
2. Identify the series by n_{1}: n_{1}=1→Lyman(UV), n_{1}=2→Balmer(visible), n_{1}=3→Paschen(IR).
3. Apply Rydberg formula: 1/λ = $RZ^{2}$(1/n_{1}^{2} − 1/n_{2}^{2}).
4. Check units: R in $m^{-1}$ → λ in metres. Convert to nm: multiply by 10^{9}.
5. Cross-check with energy: E = hc/λ = 1240 eV·nm / λ(nm).

Chain for Bohr Model Problems:

1. Identify Z and n from the problem.
2. Apply relevant formula: r = 0.529$n^{2}$/Z Å; v = $2.18 \times 10^{6}$Z/n m/s; E = −13.6$Z^{2}$/$n^{2}$ eV.
3. For ratios: Cancel common factors (a_{0}, 13.6 eV). Use proportionality: r∝$n^{2}$/Z, E∝−$Z^{2}$/$n^{2}$.
4. For KE/PE: KE = −E (positive), PE = 2E (negative). Check: KE + PE = E.
5. For ionization energy: IE = |E_n| = 13.6$Z^{2}$/$n^{2}$ eV.

Chain for Radioactive Decay Problems:

1. Find number of half-lives: n = t/t_{1}/{2} (may need to find t{1}/{2} from λ first: t{1}/_{2} = 0.693/λ).
2. Find remaining fraction: N/$N_{0}$ = (1/2)ⁿ or use N = $N_{0}$e^(−λt) for non-integer n.
3. For activity: A = λN (or use A = $A_{0}$(1/2)ⁿ).
4. For decay constant: λ = 0.693/t_{1}/_{2}.
5. For mean life: τ = 1/λ = 1.443 t_{1}/{2} (always greater than t{1}/_{2}).
6. For consecutive decays: Set up simultaneous equations from A and Z conservation.

Chain for Nuclear Physics Problems:

1. For nuclear radius: R = 1.2 × A^(1/3) fm. For ratios: $R_{1}$/$R_{2}$ = ($A_{1}$/$A_{2}$)^(1/3).
2. For binding energy: (a) Calculate $\Delta m$ = [Z·m_p + (A−Z)·m_n] − M. (b) BE = $\Delta m$ × 931.5 MeV.
3. For decay equation: Use conservation of A and Z. Alpha: A−4, Z−2. Beta-minus: A same, Z+1.
4. For consecutive decays: Let α = alpha decays, β = beta decays. Solve 2 equations from $\Delta A$ and $\Delta Z$.