Chapter 17 – Modern Physics (JEE)
1. Introduction to Modern Physics
Classical physics failed to explain phenomena like black body radiation,
photoelectric effect, and atomic stability.
Modern Physics emerged to explain microscopic world behavior.
2. Dual Nature of Radiation
Light shows both wave and particle nature.
Photoelectric Effect
Emission of electrons from a metal surface when light of suitable frequency falls on it.
Einstein’s photoelectric equation:
$$h\nu = \phi + \frac{1}{2}mv^2$$
- $h$ = Planck’s constant
- $\nu$ = frequency of incident light
- $\phi$ = work function
Key observations:
- No emission below threshold frequency
- Kinetic energy depends on frequency, not intensity
3. Threshold Frequency
$\nu_0 = \frac{\phi}{h}$
4. de Broglie Hypothesis (Matter Waves)
Every moving particle is associated with a wave.
de Broglie wavelength:
$$\lambda = \frac{h}{p} = \frac{h}{mv}$$
Confirmed experimentally by Davisson–Germer experiment.
5. Heisenberg Uncertainty Principle
$$\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$$
Position and momentum cannot be measured simultaneously with absolute precision.
6. Atomic Models
Rutherford Model
Failed to explain atomic stability.
Bohr’s Atomic Model
Angular momentum:
$$mvr = \frac{nh}{2\pi}$$
Radius of nth orbit:
$$r_n = \frac{n^2 h^2}{4\pi^2 m k e^2}$$
Energy of electron:
$$E_n = -\frac{13.6}{n^2}\,\text{eV}$$
7. Hydrogen Spectrum
$$\frac{1}{\lambda} = R\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$$
- Lyman series ($n_1=1$)
- Balmer series ($n_1=2$)
- Paschen series ($n_1=3$)
8. X-Rays
Produced when high-speed electrons strike heavy metal target.
Minimum wavelength:
$$\lambda_{min} = \frac{hc}{eV}$$
9. Nuclear Physics
Mass Defect
$$\Delta m = Zm_p + Nm_n - M$$
Binding Energy
$$E = \Delta m c^2$$
Higher binding energy → more stable nucleus.
10. Radioactivity
Spontaneous disintegration of unstable nuclei.
$$N = N_0 e^{-\lambda t}$$
Half-life:
$$T_{1/2} = \frac{0.693}{\lambda}$$
11. Nuclear Fission and Fusion
- Fission: splitting of heavy nucleus
- Fusion: combining of light nuclei
12. Semiconductors (Basic Introduction)
Materials whose conductivity lies between conductors and insulators.
| Type | Description |
|---|---|
| Intrinsic | Pure semiconductor |
| Extrinsic | Doped semiconductor |
Important for electronic devices.
13. Important JEE Formula Summary
$E = h\nu$
$\lambda = \frac{h}{mv}$
$E = mc^2$
14. Common JEE Traps
- Confusing intensity with frequency
- Ignoring threshold frequency
- Wrong unit conversions (eV ↔ J)
15. Final Revision Checklist
You are fully prepared if you can:
- Explain photoelectric effect graphically
- Derive de Broglie wavelength
- Use Bohr formulas confidently
- Solve radioactive decay problems