Electrons into hydrogen: which lines light up?

Electrons of chosen energy fired into hydrogen: which levels get excited and the emission lines that follow as atoms fall back; absorption mode with white light.

Find the lowest electron energy that makes the gas emit exactly three different lines (12.09 eV)

Assuming the energy gaps grow as n grows — the levels crowd together.

• The atom's energy is lowest (most negative) with the electron in the innermost orbit, n = 1. For n = 2, 3, … the magnitude of E shrinks, so the energy rises in the outer orbits.
• The lowest state is the ground state: n = 1, orbit radius a₀, E₁ = −13.6 eV. The least energy that frees the electron from the ground state, 13.6 eV, is the ionisation energy of hydrogen, and Bohr's prediction agrees very well with experiment.
• At room temperature most hydrogen atoms are in the ground state. Energy from collisions (for example with electrons) can lift the electron to a higher level: the atom is then in an excited state.
• E₂ = −3.40 eV, so excitation to the first excited state needs E₂ − E₁ = 10.2 eV. E₃ = −1.51 eV, so the second excited state (n = 3) needs 12.09 eV.
• From an excited state the electron can fall back to a lower level, emitting a photon. The higher the excitation (the larger n), the less energy is needed to free the electron.
• Fig. 12.7 stacks the levels as horizontal lines, numbered by n from the bottom up in order of rising energy. The top, n = ∞, has E = 0: the electron removed to infinity and at rest. The levels crowd closer together as n increases.
• Above E = 0 the electron is free and can have any energy: a continuum of states.

Teaching this idea? Put the simulation on your own page or LMS with this code.