Explaining Line Spectra | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

Discrete lines are evidence for discrete energy levels

Each spectral line has one frequency. Photon energy depends on frequency, so each line represents one photon energy. That photon energy equals a difference between two electron energy levels.

Different elements have different sets of energy levels, so they produce different line spectra. The spectrum can therefore identify the element (9702/42/O/N/22 Q9(a)(i)) (9702/42/O/N/25 Q8(a)).

One spectral line means one photon frequency.
One frequency means one photon energy through the photon-energy relation.
One photon energy means one allowed energy-level difference.
Separate lines therefore show that the atom has separate energy differences and discrete energy levels.

Worked example

Find an atomic energy level from an emitted wavelength

An electron falls to an energy level of −3.40 eV and emits a photon of wavelength 658 nm. Calculate the initial energy level in joules (9702/42/F/M/23 Q7(b)).

Calculate the photon energy.
$E_{\gamma}=\dfrac{hc}{\lambda}$
$E_{\gamma}=3.02\times10^{-19}\ \mathrm{J}$
Convert the lower level to joules.
$E_{\mathrm{low}}=-3.40\ \mathrm{eV}$
$E_{\mathrm{low}}=-5.44\times10^{-19}\ \mathrm{J}$
For emission, the initial level is higher by the photon energy.
$E_{\mathrm{high}}=E_{\mathrm{low}}+E_{\gamma}$
$E_{\mathrm{high}}=-2.42\times10^{-19}\ \mathrm{J}$

Answer

E_{\mathrm{high}}=-2.42\times10^{-19}\ \mathrm{J}

Absorption removes matching photons from the forward beam

A photon is absorbed when its energy exactly equals an allowed energy gap. The electron moves to the higher level. It later returns to a lower level and emits a photon in a random direction.

Fewer photons of the matching wavelength continue in the original direction, so a dark line appears in the transmitted spectrum. The same energy gaps create the bright emission lines and the dark absorption lines (9702/42/F/M/23 Q7(a)).

Your turnexam explanation

Why does an isolated atom not absorb every photon that reaches it?

Show worked answer

Its electrons can occupy only discrete energy levels. A photon is absorbed only when its energy exactly matches an allowed energy difference.

Learn the chain in both directions: energy levels determine photon energies and spectral lines; discrete spectral lines are evidence for discrete energy levels.