Part of JPC-07 — Atomic Structure: Quantum Numbers & Electronic Config

Bohr Model Equations

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For hydrogen-like species (one electron): rnr_n = 0.529 n2n^2/Z angstroms (radius increases with n2n^2, decreases with Z). EnE_n = -13.6 Z2Z^2/n2n^2 eV = -2.18 x 10^-18 Z2Z^2/n2n^2 J (energy is negative, becomes less negative with increasing n). vnv_n = 2.18 x 10^6 Z/n m/s (velocity decreases with n). Angular momentum LnL_n = nh2pi\frac{nh}{2*pi} (quantised in units of h-bar). Key ratios: for different species at same n: E proportional to Z2Z^2, r proportional to 1/Z, v proportional to Z. For transitions: EphotonE_{photon} = |En2E_{n2} - En1E_{n1}| = 13.6Z2Z^2|1/n12n1^2 - 1/n22n2^2| eV. Bohr model limitations: works only for one-electron species. Cannot explain: multi-electron atoms, fine structure, Zeeman effect, molecular bonding.

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