🎯 What’s Happening Inside a Hydrogen Atom?
The electron in a hydrogen atom can sit only on special “floors” of energy, labelled by the whole number n. The lowest floor (n = 1) is called the ground state; its energy is –13.6 eV. Moving the electron to higher floors (n = 2, 3, …) costs energy, so those levels sit at –3.40 eV, –1.51 eV, and so on. Freeing (ionising) the atom means supplying +13.6 eV, enough to lift the electron off the building entirely. :contentReference[oaicite:0]{index=0}
🚀 Jumps, Photons, and Bright Lines
- When an electron drops from a higher floor (ni) to a lower one (nf), it releases a packet of light (a photon). The energy—and therefore colour—of that photon is set by $$h\nu_{if}=E_{n_i}-E_{n_f}\,.$$ :contentReference[oaicite:1]{index=1}
- Emission lines 🌈: these colourful streaks appear when many atoms relax and spit out photons with exactly the energies above.
- Absorption lines 🕳️: shine a broad rainbow through cool hydrogen gas and those same energies get stolen, leaving dark gaps. :contentReference[oaicite:2]{index=2}
🔋 Energy Level Quick-Reference
| Level (n) | Energy (eV) | Jump from ground (eV) |
|---|---|---|
| 1 | –13.6 | 0 |
| 2 | –3.40 | +10.2 |
| 3 | –1.51 | +12.09 |
Notice how the floors bunch up closer together as n grows. :contentReference[oaicite:3]{index=3}
📝 Why Only Certain Colours?
Because both ni and nf are integers, the difference \(E_{n_i}-E_{n_f}\) can take only certain values. That means the frequency \( \nu \) (and wavelength \( \lambda \)) of light is locked to those discrete choices—nature’s very own barcode! :contentReference[oaicite:4]{index=4}
✨ Bohr’s Big Win
Explaining these bright-line barcodes was a triumph for Niels Bohr’s model of the atom and paved the way for modern quantum ideas. (Fun fact: the achievement earned Bohr the 1922 Nobel Prize 🏅.) :contentReference[oaicite:5]{index=5}
🔑 High-Yield Ideas for NEET
- Ground-state energy of hydrogen is –13.6 eV; ionisation energy is 13.6 eV. :contentReference[oaicite:6]{index=6}
- Photon energy from a transition follows \(h\nu = E_{n_i}-E_{n_f}\). :contentReference[oaicite:7]{index=7}
- First excited-state gap: 10.2 eV (key value for Balmer-alpha questions). :contentReference[oaicite:8]{index=8}
- Emission vs. absorption spectra concept—dark lines appear exactly where bright lines would be. :contentReference[oaicite:9]{index=9}
- Energy levels crowd together as n increases, leading to closely spaced lines at higher energies. :contentReference[oaicite:10]{index=10}
Keep practicing, and these “quantum jumps” will feel like second nature 😄!
