Modern Physics and Electronic Devices — NEET Physics

Modern physics is a small syllabus with an outsized NEET yield — a reliable 4–5 questions from a compact set of revolutionary ideas: light and matter are both particle and wave; atoms have quantised energy levels; nuclei store colossal energy; and semiconductors, engineered atom by atom, run all electronics. The formulas are few and clean, so this is one of the highest-return blocks in the paper. This chapter derives the key results, explains why each experiment forced a new idea, and drills the standard problems in full.

PART A — DUAL NATURE OF RADIATION AND MATTER

1. The photoelectric effect — the experiment

Shine light on a metal and electrons are ejected. Careful measurement gives five facts that no wave theory could explain:

1. Emission is instantaneous (no build-up time), even for faint light.
2. For each metal there is a threshold frequency $f_0$ below which no electrons come out, however intense the light.
3. The maximum kinetic energy of the electrons depends on the frequency, not the intensity.
4. The number of electrons (the photocurrent) depends on the intensity.
5. The stopping potential $V_0$ (the reverse voltage that just halts the most energetic electron) rises with frequency.

2. Einstein's photoelectric equation

Einstein resolved this by quantising light into photons of energy $E=hf$. Each photon gives all its energy to one electron; part ($\varphi$, the work function) frees it, the rest becomes kinetic energy:

$hf=\varphi +K{E}_{\max },K{E}_{\max }=hf-\varphi =h(f-f_0)$

Since the stopping potential satisfies $e{V}_0=K{E}_{\max }$:

$e{V}_0=hf-\varphi \Rightarrow V_0=\frac{h}{e}f-\frac{\varphi }{e}.$

A graph of $V_0$ against $f$ is a straight line of slope $h/e$ — the same for every metal — and an intercept fixing the work function. This clinched the photon idea and won Einstein the 1921 Nobel Prize.

• Intensity → number, frequency → energy. Doubling intensity doubles the current but leaves each electron's energy unchanged; raising frequency raises the energy.

Worked example 2.1. A metal has work function 2 eV. Light of energy 5 eV strikes it. Maximum KE of the photoelectrons? $K{E}_{\max }=hf-\varphi =5-2=3$ eV. The stopping potential is $V_0=K{E}_{\max }/e=3$ V.

3. Photon energy and momentum

$E=hf=\frac{hc}{\lambda },p=\frac{E}{c}=\frac{h}{\lambda }.$

A convenient shortcut in exam units: $E(\text{eV})=\frac{1240}{\lambda (\text{nm})}$.

• A 620 nm photon carries $E=1240/620=2$ eV.
• A photon has momentum despite being massless — the basis of radiation pressure and light sails.

4. Matter waves: de Broglie

If light waves behave as particles, particles should behave as waves. de Broglie proposed every moving particle has a wavelength:

$\lambda =\frac{h}{p}=\frac{h}{mv}=\frac{h}{\sqrt{2mK}}.$

For an electron accelerated through a potential difference $V$, $K=eV$, giving the handy formula

${\lambda }_e=\frac{12.27}{\sqrt{V(\text{volts})}}\text{A˚}.$

• Heavier or faster particles have shorter wavelengths — why an electron microscope (tiny $\lambda$) resolves far finer detail than a light microscope. The Davisson–Germer experiment (electron diffraction off a crystal) confirmed matter waves directly.

PART B — ATOMS AND NUCLEI

5. The Bohr model — postulates and derivation

Rutherford's nuclear atom was unstable in classical physics (orbiting electrons should radiate and spiral in). Bohr fixed this with three postulates:

1. Electrons orbit in stationary states without radiating.
2. Angular momentum is quantised: $mvr=\frac{nh}{2\pi }$ ($n=1,2,3,\dots$).
3. Radiation is emitted/absorbed only when an electron jumps between levels: $hf=E_i-E_f$.

Balancing the Coulomb force against the centripetal requirement and applying quantisation gives, for a hydrogen-like atom (nuclear charge $Ze$):

$r_n=0.53\frac{n^2}{Z}\text{A˚},E_n=-13.6\frac{Z^2}{n^2}\text{eV}.$

For hydrogen ($Z=1$):

• Ground state $E_1=-13.6$ eV; the ionisation energy is $+13.6$ eV.
• Radius grows as $n^2$: the second orbit is $4\times$ the first ($\approx 2.12$ Å).
• Energy of a transition $=E_{\text{high}}-E_{\text{low}}$; the $n=2\to 1$ jump releases $-3.4-(-13.6)=10.2$ eV.

Limitations: the model works only for one-electron atoms and cannot explain fine structure or intensities — but its energy-level picture is exactly what NEET tests.

6. The hydrogen spectrum

Transitions grouped by the final level form series, all captured by the Rydberg formula:

$\frac{1}{\lambda }=R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right),R=1.097\times 10^7{\text{m}}^{-1}.$

The Balmer series (jumps down to $n=2$) is the visible one you see as hydrogen's coloured lines.

7. The nucleus: size, mass defect and binding energy

• Composition: $Z$ protons and $(A-Z)$ neutrons; $A$ is the mass number.
• Size: $R=R_0{A}^{1/3}$ with $R_0=1.2$ fm, so nuclear density is essentially constant ($\sim 2.3\times 10^{17}$ kg/m³) — matter is mostly empty space with a fantastically dense core.
• Mass defect: a nucleus is lighter than its separate nucleons; the missing mass $\Delta m$ is converted to the binding energy that holds it together, via $E=\Delta m{c}^2$ (with $1\text{u}=931.5$ MeV).

The binding energy per nucleon curve rises steeply, peaks at about 8.8 MeV near iron ($A\approx 56$), then falls slowly. This single curve explains nuclear energy: fusing light nuclei or fissioning heavy ones both move toward iron and release energy.

Worked example 7.1. If 0.02 u of mass is lost when a nucleus forms, its binding energy is $0.02\times 931.5\approx 18.6$ MeV.

8. Radioactivity and the decay law

Unstable nuclei emit:

• α — a helium nucleus (${}_2^4\text{He}$): $Z\to Z-2$, $A\to A-4$. Low penetration.
• β⁻ — an electron from a neutron converting to a proton: $Z\to Z+1$, $A$ unchanged.
• γ — a high-energy photon: $Z$, $A$ unchanged (the nucleus de-excites).

Decay is random but statistically exponential:

$N=N_0{e}^{-\lambda t}=N_0{\left(\frac{1}{2}\right)}^{t/T},T_{1/2}=\frac{0.693}{\lambda },\tau =\frac{1}{\lambda }=\frac{T_{1/2}}{0.693}.$

• After $n$ half-lives, a fraction $(1/2{)}^n$ remains: $\frac{1}{4}$ after 2, $\frac{1}{8}$ after 3.
• Activity $A=\lambda N$ (decays per second, in becquerel). Carbon-14 dating and medical tracers rely on these laws.

9. Fission and fusion

• Fission: a heavy nucleus (U-235) absorbs a neutron and splits, releasing $\sim 200$ MeV and more neutrons — a controllable chain reaction (reactors) or an explosive one (bombs).
• Fusion: light nuclei (hydrogen isotopes) merge into helium, releasing even more energy per nucleon — the power source of the Sun and stars, requiring enormous temperatures.

PART C — SEMICONDUCTOR ELECTRONICS

10. Energy bands and doping

Solids have a valence band (bound electrons) and a conduction band (free to move), separated by a band gap $E_g$:

• Conductors: bands overlap ($E_g\approx 0$).
• Insulators: large gap ($E_g>3$ eV).
• Semiconductors: small gap (Si $\approx 1.1$ eV, Ge $\approx 0.7$ eV) — insulating when cold, conducting when warmed or doped.

Doping a pure (intrinsic) semiconductor tailors its conduction:

• n-type: add a pentavalent donor (P, As, Sb) → spare electrons are the majority carriers.
• p-type: add a trivalent acceptor (B, Al, Ga) → holes are the majority carriers.

The crystal stays electrically neutral overall; doping just decides which carrier dominates.

11. The p–n junction and diode

Join p- and n-type material and electrons/holes diffuse across, leaving a charged depletion region with a barrier potential (~0.7 V for Si, ~0.3 V for Ge).

• Forward bias (p to +, n to −): the barrier is lowered, and the diode conducts freely above ~0.7 V.
• Reverse bias (p to −, n to +): the barrier widens, and only a tiny leakage current flows — the diode blocks. A large enough reverse voltage causes breakdown.

A diode is thus a one-way valve for current.

12. Rectifiers and special diodes

• Rectifier: converts AC to DC. A half-wave rectifier (one diode) passes only one half of each cycle; a full-wave bridge rectifier (four diodes) uses both halves, giving smoother DC.
• Zener diode: operated in reverse breakdown at a fixed voltage — a voltage regulator.
• LED: emits light on forward conduction (energy $E_g=hf$).
• Photodiode / solar cell: light generates a current — the basis of light sensors and solar panels.

13. Logic gates (basics)

Digital electronics is built from gates acting on binary inputs (0/1):

14. Common traps NEET sets here

• Intensity vs frequency in the photoelectric effect — intensity sets the number of electrons, frequency their energy; no emission below $f_0$, however bright.
• Sign of energy levels — bound states are negative; ionisation energy is the positive amount to reach zero.
• Radius as $n^2$, energy as $1/n^2$ — don't swap; and for hydrogen-like atoms include the $Z$ factors.
• Half-life fractions — after $n$ half-lives, $(1/2{)}^n$ remains, not $1/n$.
• α and β changes — α: $A-4,Z-2$; β⁻: $Z+1$, $A$ same; γ: no change.
• Binding energy peaks at iron — both fusion (light) and fission (heavy) release energy moving toward it.
• n-type has electrons, p-type has holes — pentavalent vs trivalent doping; the crystal stays neutral.
• Diode direction — conducts only in forward bias.

15. Memory aids

• "Frequency = energy, intensity = number" — photoelectric rule.
• "1240/λ(nm) = eV" — quick photon energy.
• "−13.6 Z²/n² energy, 0.53 n²/Z radius" — the Bohr atom.
• "Balmer is the visible series."
• "Iron is most tightly bound."
• "(½)ⁿ per n half-lives; τ = T/0.693."
• "Penta → n-type electrons, tri → p-type holes."
• "Forward conducts, reverse blocks; bridge = 4 diodes."

16. Exam protocol

1. Photoelectric: $K{E}_{\max }=hf-\varphi$, $e{V}_0=hf-\varphi$; no emission below $f_0$; intensity → number, frequency → energy.
2. Photon $E=hc/\lambda =1240/\lambda (\text{nm})$ eV; momentum $p=h/\lambda$.
3. de Broglie $\lambda =h/mv$; electron through $V$: $\lambda =12.27/\sqrt{V}$ Å.
4. Bohr: $E_n=-13.6Z^2/n^2$ eV, $r_n=0.53n^2/Z$ Å; transition energy = level difference; Balmer is visible.
5. Nucleus: $R=R_0{A}^{1/3}$ (constant density); BE $=\Delta m{c}^2$, $1\text{u}=931.5$ MeV; peak at iron.
6. Decay: $N=N_0(1/2{)}^{t/T}$, $T=0.693/\lambda$; α ($A-4,Z-2$), β⁻ ($Z+1$), γ (no change).
7. Semiconductors: doping (penta → n, tri → p); diode conducts forward; bridge rectifier = 4 diodes; Zener regulates.