High-Yield Topics in Modern Physics for Competitive Exams

Introduction

Modern physics contributes 20+ marks almost every year. The theory is compact, derivations are repetitive, and numericals rely on a small formula basket. That makes it perfect for quick gains.

Background / Prerequisites

• Familiarity with basic atomic models.
• Comfort working with electron volt units and simple exponentials.

Core Concepts

• Photoelectric effect graphs and Einstein’s equation.
• Bohr model energy levels and spectral series.
• Radioactive decay law and half-life tricks.
• Semiconductor basics: intrinsic vs extrinsic, diode I-V curve.

Detailed Explanation

1. Photoelectric effect: Prepare graphs of stopping potential vs frequency and current vs intensity. Keep mental shortcuts for Planck’s constant conversions.
2. Bohr model: Memorize E_n = -13.6 eV / n^2 and the relation between wavelength and level transitions. Practice Lyman/Balmer/Paschen quick checks.
3. Radioactivity: Use \(N = N_0 e^{-\lambda t}\). Remember that activity A = lambda N. For successive decays, plan a mini table.
4. Semiconductors: Understand band diagrams qualitatively, the effect of doping, and logic gate truth tables.

Examples / Applications

• Solve a set of 10 mixed questions every time you revise this module.
• Maintain a one-page cheat sheet listing constants like h, c, e, m_e.
• Use dimensional analysis to double-check diode equations or Einstein relation units.

Common Mistakes & Tips

• Mixing joules and electron volts. Convert early and stay consistent.
• Forgetting selection rules for spectral lines (n_final < n_initial).
• Overcomplicating half-life questions; most require at most two steps.

Summary / Key Takeaways

• Modern physics rewards crisp conceptual understanding over lengthy derivations.
• Keep constants handy and set up units carefully.
• Practise small daily bursts (15 minutes) to keep formulas fresh.

Further Reading / Related Topics

• X-ray production and Moseley’s law.
• Logic gate implementations and truth tables.
• LED and photodiode characteristics.