U3.11 · Spectroscopy and the Electromagnetic SpectrumPractice · 光谱与电磁波谱

c = λν, so ν = c/λ. Convert the wavelength to meters first: 486.1 nm = $4.861 \times 10^{-7}$ m. ν = $3.0 \times 10^{8}$ ÷ $4.861 \times 10^{-7}$ = $6.17 \times 10^{14}$ Hz. Forgetting to convert nm to m puts you off by a factor of 10⁹.

E = hc/λ = $6.626 \times 10^{-34} \times 3.0 \times 10^{8}$ ÷ ($5.32 \times 10^{-7}$) = $3.74 \times 10^{-19}$ J. That is for one photon; multiply by $N_A$ for a mole of photons.

Photons from different regions carry different energies and match different kinds of motion. Microwave photons have the least energy and change rotational levels; infrared changes vibrations; visible and ultraviolet light, with more energy, move electrons to higher levels; only higher-energy UV and X-rays can ionize a molecule.

The bond energy is per mole of bonds; one bond needs 242 × 1000 ÷ ($6.022 \times 10^{23}$) = $4.019 \times 10^{-19}$ J. λ = hc/E = $6.626 \times 10^{-34} \times 3.0 \times 10^{8}$ ÷ ($4.019 \times 10^{-19}$) = $4.95 \times 10^{-7}$ m = 495 nm, which is visible light (near blue-green). That is why light alone can split $\ce{Cl2}$ into Cl atoms. Forgetting to divide by $N_A$ is off by a factor of 10²³.

E = hν = hc/λ. Doubling the wavelength halves the frequency, ν = c/λ, and halves the energy too. Longer wavelength means lower photon energy.