Atomic Spectra

15.1

Atomic / line spectra

PMDC: Describe and explain atomic spectra / line spectra.

An atom may only sit on certain energy shelves $E_n$. When an electron drops from a high shelf to a low one it emits a photon of that exact gap. So you see sharp lines, not a rainbow. A hot rarefied gas: bright lines on black (emission). A cool gas in front of a continuum: dark lines at the same wavelengths (absorption). A hot solid: a continuous smear, because packed atoms blur the shelves.

Hydrogen: $E_n$ = −13.6 / n² eV. Jumps that land on $n=1$ are Lyman (UV). On $n=2$, Balmer (visible, including red H- $\alpha$). On $n=3$, Paschen (IR). The Rydberg formula gives 1/ $\lambda$. Ionisation from the ground floor needs $13.6\mathrm{eV}$; the first excitation is $10.2\mathrm{eV}(n=1$ → 2).

• $E_n=-13.6/n^{2}eV$
• $\Delta E=E_{high}-E_{low}$ = h $f=h$ c / $\lambda$
• $1/\lambda =R(1/n_1^2-1/n_2^2)$
• Lyman: $n_1$ = 1 (UV) Balmer: $n_1$ = 2 (visible) Paschen: $n_1$ = 3 (IR)
• $H-\alpha :3\to 2\lambda \approx 656\mathrm{nm}(red)$
• $Lyman-\alpha :2\to 1\lambda \approx 122\mathrm{nm}(UV)$
• $\lambda (nm)\approx 1240/\Delta E(eV)$
• lines from level n: n(n − 1)/2