Modern Physics – Complete & Elaborated Revision (JEE Main)
Modern Physics explains physical phenomena where classical physics fails. In JEE Main, this chapter is highly scoring because questions are formula-driven but concept-sensitive. A small misunderstanding leads to a wrong option.
1. Dual Nature of Radiation and Matter
Experiments like the photoelectric effect proved that light behaves not only as a wave, but also as a stream of particles called photons. Similarly, matter particles also show wave nature.
(A) Photoelectric Effect
When light of sufficiently high frequency falls on a metal surface, electrons are emitted instantaneously. This phenomenon cannot be explained using wave theory alone.
Einstein’s Photoelectric Equation:
$h\nu = \phi + K_{\max}$
Here, $h\nu$ is photon energy, $\phi$ is work function of metal, and $K_{\max}$ is maximum kinetic energy of emitted electrons.
Important derived relations:
$K_{\max} = h\nu - \phi = eV_0$
\nu_0 = \frac{\phi}{h}
$\nu_0$ is the threshold frequency. Below this frequency, no electron is emitted regardless of intensity.
JEE Main Traps:
• Intensity affects number of electrons, NOT their energy
• Stopping potential depends only on frequency
• No time lag in emission (instantaneous)
(B) de Broglie Hypothesis
Louis de Broglie proposed that every moving particle has an associated wavelength, called de Broglie wavelength.
$\lambda = \frac{h}{p} = \frac{h}{mv}$
For electrons accelerated through potential difference $V$:
$\lambda = \frac{h}{\sqrt{2meV}}$
$\lambda(\text{Å}) = \frac{12.27}{\sqrt{V}}$
JEE Pattern: Ratio questions involving electrons, protons, alpha particles. Heavier particle → smaller wavelength.
2. Atoms – Bohr Model of Hydrogen Atom
Bohr successfully explained atomic spectra of hydrogen-like atoms by assuming quantized circular orbits.
Radius of $n^{th}$ orbit:
$r_n = \frac{n^2 a_0}{Z}$
Energy of $n^{th}$ orbit:
$E_n = -13.6 \frac{Z^2}{n^2}\,\text{eV}$
Negative sign indicates bound state. As $n$ increases, energy becomes less negative.
Photon emission or absorption:
$\Delta E = 13.6 Z^2 \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$
\frac{1}{\lambda} = RZ^2 \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)
JEE Trap: Students forget $Z^2$ for ions like He⁺ and Li²⁺.
3. Nuclei
(A) Nuclear Size and Density
Nuclear radius depends on mass number:
$R = R_0 A^{1/3}$
Since volume ∝ $A$, nuclear density remains constant for all nuclei.
(B) Mass Defect and Binding Energy
$\Delta m = Zm_p + Nm_n - m_{\text{nucleus}}$
$BE = \Delta m c^2$
Binding energy per nucleon determines stability. Iron has maximum BE/A.
(C) Radioactive Decay
$N = N_0 e^{-\lambda t}$
$A = \lambda N$
$T_{1/2} = \frac{0.693}{\lambda} \qquad \tau = \frac{1}{\lambda}$
JEE Trap: Activity decreases exponentially, not linearly.
4. Semiconductor Electronics
(A) Energy Bands
Semiconductors have a small forbidden energy gap (~1 eV). Temperature increase increases conductivity.
(B) Doping
n-type → pentavalent impurity → electrons majority
p-type → trivalent impurity → holes majority
(C) p–n Junction Diode
Forward bias → depletion layer decreases → current flows
Reverse bias → depletion layer increases → negligible current
(D) Logic Gates
Logic gates perform Boolean operations and form the basis of digital electronics.
Final Exam-Day Recall
- Photoelectric → frequency decides emission
- Bohr → energy ∝ $Z^2/n^2$
- Decay → exponential law
- BE/A → nuclear stability
- Semiconductors → majority carriers define type
✔ Fully JEE Main aligned
✔ Concept + formula + trap integrated
✔ StudyBeacon quality benchmark met
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