Summary of "🔥 Modern Physics ZERO to PYQs. JEE Main 2026."

Summary of “🔥 Modern Physics ZERO to PYQs. JEE Main 2026.”

This comprehensive lecture covers the entire Modern Physics chapter relevant for JEE Main preparation, starting from fundamental concepts to detailed problem-solving of previous years’ questions (PYQs). The instructor systematically explains key topics, important formulas, conceptual understanding, and typical JEE question patterns with step-by-step solutions.

Main Topics Covered & Key Concepts

1. Rutherford Scattering and Atomic Model

Rutherford’s gold foil experiment showed alpha particles scattering at various angles.
Proposed nuclear model: a small, positively charged nucleus with electrons revolving around it.
Coulomb repulsion causes deflection of alpha particles.
Important formula for scattering angle (Δ): [ \tan\left(\frac{\Delta}{2}\right) = \frac{k q q’}{m v_0^2 b} ] where
- (q) = alpha particle charge
- (q’) = nucleus charge
- (m) = mass of alpha particle
- (v_0) = initial velocity
- (b) = impact parameter
- Graph of number of scattered particles vs scattering angle: number decreases with increasing angle.
- PYQ example: Ratio of impact parameters for scattering angles 60° and 90° (JEE 2022).

2. Bohr’s Atomic Model

Electrons revolve in quantized orbits with quantized angular momentum: [ m v r = \frac{n h}{2 \pi} ]
Centripetal force balance: [ \frac{k Z e^2}{r^2} = \frac{m v^2}{r} ]
Radius of nth orbit: [ r_n \propto \frac{n^2}{Z} ]
Velocity proportionality: [ v \propto \frac{Z}{n} ]
Energy levels: [ E_n = -13.6 \frac{Z^2}{n^2} \text{ eV} ]
Electron transitions emit photons with energy equal to difference in energy levels.
Photon wavelength relates to energy by: [ E = h \nu = \frac{hc}{\lambda} ]
Rydberg formula: [ \frac{1}{\lambda} = R Z^2 \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right) ]
Series naming by final orbit:
- Lyman (n₁=1)
- Balmer (n₁=2)
- etc.
PYQs on velocity ratios, radius ratios, wavelength calculations, and spectral line counts.
Number of spectral lines from nth level: [ \binom{n}{2} = \frac{n(n-1)}{2} ]

3. Photoelectric Effect

Electrons emitted from metal surface when illuminated by light above threshold frequency ( \nu_0 ).
Maximum kinetic energy of emitted electrons: [ K_{\max} = h \nu - \phi ] where (\phi) = work function.
Threshold frequency: [ \nu_0 = \frac{\phi}{h} ]
Graphs discussed:
- Photoelectric current vs voltage (saturation current and stopping potential).
- Stopping potential vs frequency (linear with slope (h/e)).
- Saturation current vs intensity (directly proportional).
PYQs on kinetic energy doubling, stopping potential changes with wavelength, and intensity effects.

4. Matter Waves (de Broglie Wavelength)

Particles have wave-like properties; wavelength given by: [ \lambda = \frac{h}{p} = \frac{h}{mv} ]
Expressed in terms of kinetic energy: [ \lambda = \frac{h}{\sqrt{2 m K.E.}} ]
Important: Use photon energy formula (E=hc/\lambda) only for photons, not matter waves.
PYQs on comparing wavelengths of particles accelerated through the same potential, and wavelength changes under electric fields.

5. Radiation Pressure

Photons have momentum (p = \frac{h}{\lambda}).
Force on perfectly reflecting surface due to photons: [ F = \frac{2P}{c} ] where (P) = power of incident radiation.
Pressure on perfectly reflecting surface: [ P = \frac{2I}{c} ] where (I) = intensity.
For perfectly absorbing (black) surface, pressure is half: [ P = \frac{I}{c} ]
PYQs on calculating radiation pressure from given power and distance.

6. X-rays and Coolidge Tube

Electrons accelerated and collide with metal target producing X-rays.
Two types of X-rays:
- Continuous (bremsstrahlung) due to deceleration of electrons.
- Characteristic X-rays due to electronic transitions inside metal atoms (Kα, Kβ, Lα, etc.).
Cut-off wavelength corresponds to maximum photon energy, related to accelerating voltage.
Moseley’s law: [ \sqrt{\nu} = a(Z - b) ] where (Z) = atomic number.
Characteristic X-ray energies depend on metal, continuous X-rays depend on accelerating voltage.

7. Nuclear Physics

Nuclear radius: [ R = R_0 A^{1/3} ] with (R_0 \approx 1.1-1.2 \, \text{fm}).
Nuclear density approximately constant across nuclei.
Binding energy (BE): energy required to break nucleus into protons and neutrons.
Mass defect (\Delta m) leads to binding energy: [ BE = \Delta m c^2 ]
Binding energy per nucleon indicates stability; Fe-56 has maximum stability.
Q-value of nuclear reaction: [ Q = BE_{\text{products}} - BE_{\text{reactants}} = (m_{\text{reactants}} - m_{\text{products}}) c^2 ]
PYQs on calculating Q-values, binding energies, and nuclear densities.

8. Radioactivity

Decay law: [ \frac{dN}{dt} = -\lambda N ]
Solution: [ N = N_0 e^{-\lambda t} ]
Activity (A = \lambda N), units: disintegrations per second (Becquerel), Curie defined as (3.7 \times 10^{10}) Bq.
Half-life: [ T_{1/2} = \frac{\ln 2}{\lambda} ]
Effective decay constant for simultaneous decay processes: [ \lambda_{\text{eff}} = \lambda_1 + \lambda_2 ]
PYQs on half-life calculations, activity ratios, and combined decay processes.

Methodologies & Important Formulae

Rutherford Scattering: Use formula for scattering angle involving impact parameter. Understand inverse proportionality between scattering angle and impact parameter.
Bohr Model: Write centripetal force and quantization of angular momentum equations. Derive radius and velocity relations. Use energy level formula for transitions. Apply Rydberg formula for spectral lines and series. Count spectral lines using combination formula ( \frac{n(n-1)}{2} ).
Photoelectric Effect: Use (K_{\max} = h\nu - \phi). Identify threshold frequency. Analyze graphs of current vs voltage, stopping potential vs frequency. Calculate changes in stopping potential or kinetic energy for different wavelengths.
Matter Waves: Calculate de Broglie wavelength using momentum or kinetic energy. Compare particle and photon wavelengths carefully.
Radiation Pressure: Calculate force and pressure from incident power or intensity. Differentiate between reflecting and absorbing surfaces.
X-rays: Identify continuous and characteristic X-rays. Use accelerating voltage to find cut-off wavelength. Apply Moseley’s law for frequency vs atomic number.
Nuclear Physics: Calculate nuclear radius and understand constant density. Use mass defect and binding energy relations. Compute Q-values from binding energies or mass differences.
Radioactivity: Solve decay differential equation. Use half-life and activity formulas. Calculate effective decay constants for multiple decay modes.

Speakers / Sources Featured

Primary Speaker: The instructor (name not mentioned), who explains the concepts and solves JEE Main previous years’ questions with detailed reasoning and formula derivations.

This summary covers the essential ideas, formulas, and problem-solving approaches for Modern Physics in JEE Main, as presented in the video. The focus is on understanding fundamental principles, memorizing key formulas, and applying them effectively to solve typical exam questions.