Atomic Structure – Complete Conceptual & Numerical Revision
Atomic Structure explains why atoms behave the way they do. JEE doesn’t test history — it tests quantization, wave–particle duality, hydrogen spectrum logic, and hidden unit traps.
1. Fundamental Picture of Atom
Atom consists of nucleus (protons + neutrons) surrounded by electrons. Classical physics fails → quantum concepts required.
Key Idea: Electron does NOT move in a classical orbit — it exists as a probability wave
2. Photoelectric Effect (Concept + Formula)
When light of frequency ≥ threshold frequency strikes a metal, electrons are ejected.
$E = h\nu$
$h\nu = h\nu_0 + KE_{max}$
$KE_{max} = \frac{1}{2}mv^2 = h(\nu - \nu_0)$
JEE Trap: Intensity affects number of electrons, NOT their kinetic energy
3. Dual Nature of Matter (de Broglie)
Every moving particle behaves like a wave.
$\lambda = \dfrac{h}{p} = \dfrac{h}{mv}$
$\lambda = \dfrac{h}{\sqrt{2mKE}}$
Trap: Electron wavelength ≠ EM wavelength
4. Bohr’s Model (Hydrogen-like Species)
Applicable ONLY to one-electron systems: H, He⁺, Li²⁺ …
Radius of nth orbit:
$r_n = \dfrac{n^2 a_0}{Z}$
Energy of nth orbit:
$E_n = -\dfrac{13.6 Z^2}{n^2} \text{ eV}$
Velocity of electron:
$v_n = \dfrac{Z}{n} \times 2.18 \times 10^6 \, m/s$
Major Trap: Negative energy means bound state, not “low energy”
5. Hydrogen Spectrum & Rydberg Formula
Spectral lines arise due to electronic transitions.
$\frac{1}{\lambda} = RZ^2\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$
Series:
- Lyman (UV): $n_1 = 1$
- Balmer (Visible): $n_1 = 2$
- Paschen (IR): $n_1 = 3$
Trap: Shortest wavelength → highest energy transition
6. Quantum Numbers (Frequently Tested)
| Quantum No. | Symbol | Possible Values |
|---|---|---|
| Principal | $n$ | 1,2,3,... |
| Azimuthal | $l$ | 0 to (n−1) |
| Magnetic | $m_l$ | −l to +l |
| Spin | $m_s$ | ±½ |
Trap: For s-orbital, $l=0$ ⇒ only one orientation
7. Heisenberg Uncertainty Principle
$\Delta x \cdot \Delta p \ge \dfrac{h}{4\pi}$
Cannot know position and momentum simultaneously with certainty.
Conceptual Trap: Not due to instrument limitation — fundamental nature of matter
8. How JEE Main Tries to Fool You
- Mixing classical & quantum logic
- Wrong unit conversions (Joule ↔ eV)
- Applying Bohr to multi-electron atoms
- Sign errors in energy values
Memory Anchor:
One electron → Bohr valid
Many electrons → Bohr fails
✔ NCERT aligned
✔ JEE Main 2026 ready
✔ Conceptual + numerical balanced
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