recall and use hf = E1 – E2

Key Equation: \$hf = E1 - E2\$

Here \$h\$ is Planck's constant (≈ \$6.626 \times 10^{-34}\$ J·s), \$f\$ is the frequency of the photon, and \$E1\$ and \$E2\$ are the energies of the two atomic levels involved. When an electron jumps from a higher level \$E2\$ to a lower level \$E1\$, it emits a photon with energy \$hf\$.

Analogy: The Electron Ladder 🚶‍♂️

Think of an atom as a ladder with rungs (energy levels). An electron is a person climbing up or down. When the person jumps down, they drop a small amount of energy, like dropping a pebble that makes a sound. That sound is the photon we see as light. The higher the jump, the louder (more energetic) the sound!

Example: Hydrogen Balmer Line (Hα)

For hydrogen, the Balmer series involves transitions from \$n=3\$ to \$n=2\$.

Energy difference: \$ΔE = E2 - E3 = (-3.40) - (-1.51) = -1.89\$ eV (negative sign indicates emission).

Convert to frequency: \$f = \frac{ΔE}{h}\$, then wavelength: \$\lambda = \frac{c}{f}\$.

Result: \$\lambda ≈ 656\$ nm (red light).

Exam Tip 📚

• Always write the equation \$hf = E1 - E2\$ and remember that \$E_1\$ is the lower level.
• Use \$ΔE = h f\$ to find frequency, then \$\lambda = \frac{c}{f}\$.
• Check units: eV → J (multiply by \$1.602\times10^{-19}\$).
• Remember common series: Lyman (\$n=1\$), Balmer (\$n=2\$), Paschen (\$n=3\$).
• When given wavelength, you can reverse the steps to find \$ΔE\$.

Quick Formula Sheet ✨

1. \$hf = E1 - E2\$
2. \$ΔE = h f\$
3. \$f = \frac{c}{\lambda}\$
4. \$\lambda = \frac{c}{f}\$
5. \$E_n = -\frac{13.6\,\text{eV}}{n^2}\$ for hydrogen

Keep practising with different \$n\$ values to become comfortable!