Atoms
The Atoms chapter covers Rutherford's alpha-scattering conclusions, Bohr's postulates, radii and energies of hydrogen levels, and the spectral series. Expect a numerical on transition energy or the radius of an orbit.
Core rules
- Rutherford: most alpha particles pass undeflected, a few deflect strongly, implying a tiny massive positive nucleus with most of the atom empty.
- Bohr postulates: quantised angular momentum mvr = nh/2π; electrons in stationary orbits do not radiate; emission or absorption occurs on transition with hν = E₂ − E₁.
- Radius r(n) = 0.53 n²/Z Å; velocity v(n) = 2.18×10⁶ Z/n m/s.
- Energy E(n) = −13.6 Z²/n² eV; the negative sign means the electron is bound.
- Ionisation energy of hydrogen from the ground state is 13.6 eV; the first excitation energy is 10.2 eV.
- Series: Lyman (to n = 1, ultraviolet), Balmer (to n = 2, visible - Hα 656 nm), Paschen, Brackett, Pfund (infrared).
- Rydberg: 1/λ = R(1/n₁² − 1/n₂²), R = 1.097×10⁷ m⁻¹.
Worked example
For the transition n = 3 to n = 2 in hydrogen: ΔE = 13.6(1/4 − 1/9) = 13.6 × 0.1389 = 1.89 eV. Then λ = 1240/1.89 ≈ 656 nm, the red Hα line of the Balmer series. The radius of the n = 2 orbit is 0.53 × 4 = 2.12 Å.
Traps
- Taking the energy as positive and then getting a negative wavelength.
- Confusing the ionisation energy (13.6 eV) with the first excitation energy (10.2 eV).
- Assigning Balmer lines to the ultraviolet region; they are visible.