Excitation, Binding, and Ionization
Excitation energy is E_f - E_i for two bound levels with E_f > E_i. Ionization energy from level n is 0 - E_n = |E_n|. In collision excitation, the projectile must supply at least the required gap, with excess energy shared consistently.
Why this shows up in the exam
Finding threshold bombarding voltage · Ionizing excited hydrogen-like ions · Determining accessible levels from supplied energy
Learn the idea
Excitation moves an electron between bound levels; ionization raises it to the zero-energy continuum. A bound electron must receive exactly an allowed level gap to settle in another stationary state. Giving at least its binding energy can free it.
🧠 Memory hook: Excitation stops on a rung; ionization leaves the ladder.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Delta E_exc = 13.6 Z² (1/n_i² - 1/n_f²) eV — energy absorbed for n_f greater than n_i
- E_ion(n) = 13.6 Z²/n² eV — ionization energy from level n
- e V_min = Delta E — minimum electron-acceleration voltage for a specified excitation
How to approach it
- 1Write signed initial and final energies
- 2Take final minus initial for absorbed energy
- 3Compare supplied energy with the exact gap or continuum threshold
Common slip-ups that cost marks
- •Using 13.6 eV for every ion and every level
- •Assuming any sub-threshold photon energy can accumulate in one isolated atom
- •Confusing excitation energy with final level energy
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
In hydrogen, an electron transitions from n = 2 to n = 1. Using E_n = -13.6/n^2 eV, find the emitted photon energy.
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