Energy levels and atomic spectra

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An atom can only have certain **fixed** allowed energies — never the values in between (like stairs, not a ramp).

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A single tiny **packet of light energy**. Its energy is given by E = hf = hc/λ.

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It **emits a photon** whose energy equals the **gap** between the two levels (an emission line).

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An electron **jumps up** to a higher level — but only if the photon's energy exactly matches a level **gap**.

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$E = hf$ — energy = Planck constant × frequency (given in the data booklet).

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$E = \dfrac{hc}{\lambda}$ — bigger energy means shorter wavelength (given).

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The one with the **smallest** energy drop — because E = hc/λ, a small energy means a large wavelength.

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The **biggest** energy drop — more energy means a shorter wavelength (and higher frequency).

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**n(n − 1) ÷ 2** distinct wavelengths. E.g. n = 3 → 3 lines; n = 4 → 6 lines.

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Emission = **bright lines** on dark (electron falls, photon out). Absorption = **dark lines** in a rainbow (electron rises, photon in). Same atom → same line positions.

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Each element has its **own** set of energy levels, so its own unique pattern of lines — you can match a spectrum to an element.

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λ = hc/E = (6.63 × 10⁻³⁴ × 3.00 × 10⁸) / (3.0 × 10⁻¹⁹) ≈ 6.6 × 10⁻⁷ m.