🌈 12.3 Atomic Spectra — Friendly Notes

1. Why do atoms glow in specific colours? 🔬

When a low-pressure gas is excited (for example, by an electric discharge), its atoms jump to higher energy states. As they return to lower states, they emit light of only a few, very precise wavelengths. Looking through a spectroscope, you see bright, razor-thin lines on a dark background — an emission-line spectrum 🌟. :contentReference[oaicite:0]{index=0}

2. Emission vs Absorption 🤔

  • Emission spectrum: Bright lines produced by excited atoms.
  • Absorption spectrum: If white light is shone through the same gas, those exact wavelengths are missing, giving dark lines at the very same positions. It’s like the gas saying, “I block what I can emit!” 😄 :contentReference[oaicite:1]{index=1}
  • Because every element has its own unique set of lines, spectra act as chemical “fingerprints” for identifying substances — handy in labs and in astronomy 🔍.

3. Linking spectra to atomic structure ⚙️

Hydrogen’s bright-line pattern (shown in Fig. 12.5 of the text) fired the imagination of early physicists and hinted that electrons occupy discrete orbits rather than sliding smoothly toward the nucleus. Continuous radiation predicted by classical physics simply doesn’t show up — reality prefers neat lines! :contentReference[oaicite:2]{index=2}

4. Quick recap of electron energy in hydrogen 🪐

Even before discussing spectra, the chapter reminds us of some key results for an electron of charge e, mass m, orbit radius r, and speed v:

  • Balance of forces gives \( \displaystyle m v^{2} = \frac{e^{2}}{4\pi\varepsilon_{0} r} \) (12.3)
  • Kinetic energy \( \displaystyle K = \tfrac12 m v^{2}= \frac{e^{2}}{8\pi\varepsilon_{0} r} \)
  • Potential energy \( \displaystyle U = -\frac{e^{2}}{4\pi\varepsilon_{0} r} \)
  • Total energy \( \displaystyle E = K + U = -\frac{e^{2}}{8\pi\varepsilon_{0} r} \) (12.4)

The negative sign means the electron is bound (it won’t fly off unless it gains at least 13.6 eV 👍). :contentReference[oaicite:3]{index=3}

✨ Worked Example (Example 12.3)

Given: Energy required to free the electron = 13.6 eV (that is, E = −13.6 eV).
Find: Orbit radius and speed.

Using \( r = -\dfrac{e^{2}}{8\pi\varepsilon_{0}E} \) you get \( r \approx 5.3 \times 10^{-11}\,\text{m} \) (the famous Bohr radius). Plugging this into \( v = \dfrac{e}{4\pi\varepsilon_{0} m r} \) gives \( v \approx 2.2 \times 10^{6}\,\text{m s}^{-1} \). 🚀 :contentReference[oaicite:4]{index=4}

Important Concepts for NEET 📝

  1. Emission vs Absorption Spectra — recognise how dark and bright lines correspond to the same wavelengths.
  2. Element Identification — each element’s line pattern acts as a spectral fingerprint.
  3. Quantised Energies — discrete lines imply discrete electron energy levels; a key jump to quantum theory.
  4. Hydrogen Spectrum — the simplest atom provides clean data for theory questions (e.g., Balmer lines in the visible range).

✨ Keep these ideas handy — they pop up again and again in NEET questions. Happy studying! ✨