Bohr model and quantized energy levels (HL)

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$E_n = -\dfrac{13.6}{n^2}$ eV, with n = 1, 2, 3, … The levels are **discrete** (quantized).

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The zero is set at the just-free electron (n → ∞), so any **bound** electron has **less** energy — hence negative.

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n = 1, with $E_1 = -13.6$ eV — the **lowest** (most tightly bound) level.

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$E_2 = -13.6/4 = -3.40$ eV.

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$hf = E_i - E_f$ — the photon energy equals the size of the energy drop.

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**Emission**: electron jumps **down**, atom gives out a photon. **Absorption**: electron jumps **up**, atom takes a photon in.

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Its levels are **discrete**, so only certain energy drops — and hence certain photon energies — are possible.

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**13.6 eV** — the energy to lift the electron from the ground state (−13.6 eV) up to 0 eV (free).

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$(-1.51) - (-3.40) = 1.89$ eV $= 3.0\times10^{-19}$ J.

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Multiply by $1.60\times10^{-19}$ (1 eV = 1.60×10⁻¹⁹ J).

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The one with the **largest** energy drop — falling down to n = 1.

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The gaps **shrink** (1/n²), so the levels **crowd together** approaching 0 eV.