Why is hydrogen's ground-state energy negative, and how much energy ionises it?
We define a stationary electron and proton infinitely far apart as zero energy.
We define a stationary electron and proton infinitely far apart as zero energy. In the atom their attraction makes total energy lower, so E_1 = -13.6 eV. To ionise from the ground state, energy must raise the electron from -13.6 eV to 0 eV, requiring +13.6 eV. From level n, the required energy is the magnitude 13.6/n^2 eV for hydrogen.
Key point
Ionisation energy from a level is the positive magnitude of that level's negative energy.
Common mistake
answering -13.6 eV for energy that must be supplied.
Memory tip
bound is below zero; pay enough energy to climb to zero.
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