Modern Physics & Semiconductors
Practice JEE Main Photoelectric effect, Bohr Model, Nuclear Physics & Semiconductor Diodes PYQs online. Includes de Broglie shortcuts & 4-step solutions.
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4-Step Solution & Tricks
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🎯 High-Yield Syllabus Breakdown
These high-frequency concepts account for over 90% of all questions asked in Modern Physics & Semiconductors:
- Photoelectric Effect & Einstein Equation: e V₀ = h ν - Φ₀
- de Broglie Wavelength: λ = h / p = 1.227 / √V nm (for electrons)
- Bohr Model of Hydrogen Atom: r_n ∝ n²/Z, E_n = -13.6 Z²/n² eV
- Radioactive Decay Law N = N₀ (1/2)^n & Half-life T_half
- Nuclear Binding Energy Curve (Iron ⁵⁶Fe maximum at 8.8 MeV/nucleon)
- Semiconductor Diodes (Forward/Reverse Bias) & Zener Diode Voltage Regulator
⚡ Essential Formulas & Speed Shortcuts
Formulas and time-saving shortcuts to solve Modern Physics questions in under 45 seconds:
Electron de Broglie Wavelength: λ = 12.27 / √V Å = 1.227 / √V nm.
First excitation energy of Hydrogen: ΔE = E₂ - E₁ = -3.4 - (-13.6) = 10.2 eV.
Zener diode operates in reverse breakdown to regulate DC output voltage.
📖 Sample Solved Exam Questions
Preview authentic questions from this chapter with full step-by-step solutions:
💡 View Step-by-Step Solution & Answer
Correct Answer: 1.227 / √V nm
- Step 1: de Broglie wavelength is λ = h / p = h / √(2 m e V).
- Step 2: Substitute Planck's constant h = 6.626 × 10⁻³⁴ J·s, m_e = 9.11 × 10⁻³¹ kg, e = 1.6 × 10⁻¹⁹ C.
- Step 3: λ = (6.626 × 10⁻³⁴) / √(2 × 9.11 × 10⁻³¹ × 1.6 × 10⁻¹⁹ × V).
- Step 4: Simplifying yields λ = (12.27 / √V) Å = 1.227 / √V nm.
⚡ Speed Tip: Standard electron formula: λ = 12.27 / √V Å = 1.227 / √V nm. For V = 100 V: λ = 0.1227 nm.
💡 View Step-by-Step Solution & Answer
Correct Answer: e V₀ = h ν - Φ₀
- Step 1: Einstein's photoelectric equation is K_max = h ν - Φ₀, where Φ₀ is the work function.
- Step 2: Stopping potential V₀ is the potential required to stop the most energetic photoelectron.
- Step 3: Maximum kinetic energy is related to stopping potential by K_max = e V₀.
- Step 4: Equating gives e V₀ = h ν - Φ₀.
⚡ Speed Tip: Photoelectric equation: e V₀ = h ν - h ν₀ = h ν - Φ₀.
💡 View Step-by-Step Solution & Answer
Correct Answer: 1 : 4
- Step 1: Bohr's formula for radius of n-th orbit is r_n = 0.529 (n² / Z) Å.
- Step 2: For hydrogen atom, atomic number Z = 1, so r_n ∝ n².
- Step 3: For n = 1: r₁ ∝ 1² = 1. For n = 2: r₂ ∝ 2² = 4.
- Step 4: Ratio of radii: r₁ : r₂ = 1 : 4.
⚡ Speed Tip: Bohr radius: r ∝ n² / Z. Doubling principal quantum number quadruples orbital radius.
❓ Frequently Asked Questions (FAQs)
Why is Modern Physics considered the highest scoring section in JEE Main?
Modern Physics questions are direct formula-based, have predictable patterns (photoelectric, Bohr model, de Broglie), and carry 12 to 16 marks per shift.