Modern Physics Basics Questions for NDA

Photoelectric Effect

When light falls on a metal surface, electrons are emitted. This only happens if the light frequency is above a minimum value called the threshold frequency. Einstein explained this using the idea that light travels in packets called photons. Each photon has energy equal to hf. If this energy is enough to pull out the electron (called work function), the electron escapes with some leftover kinetic energy. Key point: intensity of light increases the number of electrons, but increasing frequency increases their kinetic energy.

• Photon energy E = hf = hc/lambda
• Work function (phi) is the minimum energy needed to release an electron
• Kinetic energy of emitted electron = hf - phi
• Stopping potential (Vs) is voltage needed to stop the fastest electron: eVs = hf - phi
• Photoelectric effect proves particle nature of light
• No time delay in emission — instant response once threshold is crossed

Atomic Models

Thomson imagined the atom as a pudding with electrons embedded in a positive mass. Rutherford's gold foil experiment showed most of the atom is empty space and all positive charge is in a tiny nucleus. Bohr improved this by saying electrons orbit in fixed energy levels and emit or absorb light only when jumping between levels. Remember: Rutherford could not explain why orbiting electrons do not spiral into the nucleus — that is Bohr's fix.

• Thomson model: plum pudding — electrons in a sea of positive charge
• Rutherford: nucleus is small, dense, positively charged; most atom is empty
• Bohr: electrons orbit in fixed shells; energy is quantized
• Electron jumps from higher to lower shell: photon emitted
• Electron absorbs photon: jumps to higher shell
• Bohr model works well only for hydrogen-like atoms (one electron)

Dual Nature of Matter and de Broglie Wavelength

Einstein showed light behaves as both wave and particle. Louis de Broglie extended this idea and said moving particles also have a wavelength. The faster or heavier the particle, the shorter its wavelength. This wave nature matters at atomic scales but is negligible for everyday objects like a cricket ball.

• de Broglie wavelength lambda = h / mv = h / p
• Heavier or faster particles have smaller wavelength
• Electrons show wave nature in diffraction experiments
• This concept is the foundation of quantum mechanics
• NDA asks direct formula application or conceptual comparison questions

Radioactivity and Nuclear Reactions

Unstable nuclei emit radiation to become more stable. Three types: alpha (helium nucleus, 2 protons 2 neutrons), beta (electron emitted from nucleus), and gamma (high energy photon, no mass or charge change). Half-life is the time for half the sample to decay. NDA loves half-life calculation questions — they are simple once you know the formula. Nuclear fission is splitting a heavy nucleus; fusion is joining light nuclei. Both release enormous energy via E = mc^2.

• Alpha decay: mass number drops by 4, atomic number drops by 2
• Beta decay: atomic number increases by 1, mass number unchanged
• Gamma emission: no change in mass or atomic number, just energy released
• Half-life T: after n half-lives, remaining amount = N0 x (1/2)^n
• Fission: uranium splits into smaller nuclei plus neutrons and energy
• Fusion: hydrogen nuclei combine to form helium — powers the Sun

• Confusing intensity with frequency in photoelectric effect. More light intensity means more electrons, NOT faster electrons. Only higher frequency increases kinetic energy.
• In alpha decay, forgetting to reduce BOTH mass number by 4 AND atomic number by 2. Students often change only one.
• In half-life problems, dividing total time by 2 instead of dividing by half-life to get number of half-lives first.
• Mixing up emission and absorption spectra logic — electron going DOWN emits photon, going UP absorbs photon.
• Applying Bohr energy formula En = -13.6/n^2 eV to multi-electron atoms. It only works for hydrogen and hydrogen-like ions.

• ABG for radiation penetration: Alpha stopped by paper, Beta by aluminum, Gamma needs lead. Remember A-B-G = Always Buy Gold.
• Bohr energy levels: think of floors in a building. Electron falls from higher floor to lower floor and releases a photon like dropping a ball. It must absorb energy to go UP.
• Photoelectric effect mnemonic: FINE — Frequency determines If electrons come out, Not intensity, Energy = hf.
• Half-life table trick: 1 half-life = 1/2 left, 2 = 1/4, 3 = 1/8, 4 = 1/16. Just keep halving. Draw this as a quick table in rough work.

• NDA typically asks 2-3 direct formula questions: photon energy, half-life remaining amount, or de Broglie wavelength. These take under 60 seconds each if formula is memorized.
• Conceptual MCQs on which model explained what — Rutherford vs Bohr is a classic comparison question. Know what each model failed to explain.
• Alpha, beta, gamma properties table is almost always tested. Know penetrating power, ionizing power, and what changes in the nucleus for each.
• Fission vs Fusion conceptual difference appears frequently in GAT Physics. Fission = splitting heavy atom (uranium, plutonium). Fusion = combining light atoms (hydrogen). Sun runs on fusion.
• Do not spend more than 90 seconds on any Modern Physics numerical. If the numbers are messy, mark and move — most NDA Modern Physics numericals use clean numbers.