JEE Physics — Modern Physics Complete Chapter Guide

Chapter Overview & Weightage

Modern Physics is one of the most reliable scoring chapters in JEE Main. Every single year, without exception, 2–3 questions appear from this chapter. That’s 8–12 marks sitting there — and most of them are formula-based, not concept-heavy.

Modern Physics consistently contributes 8–10% of the Physics section in JEE Main. In JEE Advanced, expect 1–2 questions that test conceptual depth, particularly in nuclear physics and the photoelectric effect.

Year	JEE Main Questions	Topics Tested
2024	3	Photoelectric effect, Bohr model, Radioactivity
2023	2	Nuclear binding energy, de Broglie wavelength
2022	3	Photoelectric effect, X-ray wavelength, Half-life
2021	2	Bohr model energy levels, Radioactive decay law
2020	3	Work function, Nuclear fission, de Broglie
2019	2	Hydrogen spectrum, Half-life problems

The pattern is clear: Photoelectric Effect and Radioactivity together account for roughly 60% of all Modern Physics questions in JEE Main over the last five years. Prioritise these two, then layer in Bohr Model.

Key Concepts You Must Know

Ranked by exam frequency — spend your time accordingly.

Tier 1 (High Frequency — master these first)

Photoelectric effect: threshold frequency, stopping potential, saturation current relationships
Einstein’s photoelectric equation: $KE_{max} = h\nu - \phi$
Bohr model: energy levels of hydrogen, spectral series (Lyman, Balmer, Paschen)
Radioactive decay law: $N = N_0 e^{-\lambda t}$ , half-life, mean life relationships
Nuclear binding energy and mass defect

Tier 2 (Medium Frequency — know the key results)

de Broglie wavelength and wave-particle duality
Davisson-Germer experiment (qualitative)
X-ray production: minimum wavelength $\lambda_{min} = hc/eV$
Q-value of nuclear reactions
Successive disintegration (parent-daughter decay)

Tier 3 (Low Frequency — skim for concepts)

Nuclear fission and fusion (mostly qualitative)
Nuclear reactor principles
Carbon dating (conceptual only, rarely numerical)

Important Formulas

KE_{max} = h\nu - \phi = eV_s

When to use: Any problem involving stopping potential, threshold frequency, or maximum kinetic energy of emitted electrons. The stopping potential $V_s$ directly gives you $KE_{max}$ in eV — don’t convert unnecessarily.

$\phi = h\nu_0$ where $\nu_0$ is the threshold frequency.

E_n = -\frac{13.6}{n^2} \text{ eV} \quad \text{(for hydrogen)}

r_n = 0.529 \times n^2 \text{ Å} \quad \text{(for hydrogen)}

When to use: Energy of emitted/absorbed photons between levels: $\Delta E = E_{higher} - E_{lower}$ . For hydrogen-like ions (He⁺, Li²⁺), multiply by $Z^2$ : $E_n = -13.6Z^2/n^2$ eV.

N(t) = N_0 e^{-\lambda t} = N_0 \left(\frac{1}{2}\right)^{t/T_{1/2}}

T_{1/2} = \frac{\ln 2}{\lambda} \approx \frac{0.693}{\lambda}, \quad \tau_{mean} = \frac{1}{\lambda} = \frac{T_{1/2}}{0.693}

When to use: All decay problems. Remember: mean life $\tau = 1.44 \times T_{1/2}$ . This ratio appears directly in options sometimes.

\lambda = \frac{h}{mv} = \frac{h}{\sqrt{2mKE}} = \frac{h}{\sqrt{2meV}}

When to use: The third form is most useful in JEE — when a particle is accelerated through potential difference $V$ , use $\lambda = h/\sqrt{2meV}$ directly.

\Delta m = [Zm_p + (A-Z)m_n] - M_{nucleus}

BE = \Delta m \times 931.5 \text{ MeV/u}

When to use: Q-value problems and stability comparisons. Higher BE/nucleon = more stable nucleus. Iron-56 has the highest BE/nucleon (~8.8 MeV).

Solved Previous Year Questions

PYQ 1 — Photoelectric Effect (JEE Main 2024, Shift 1)

Question: Light of frequency $1.5\nu_0$ is incident on a metal with threshold frequency $\nu_0$ . If the intensity is doubled, the stopping potential will:

(A) Double (B) Remain the same (C) Become half (D) Increase by $0.5h\nu_0/e$

Solution:

Stopping potential comes from Einstein’s equation: $eV_s = h\nu - h\nu_0$ .

Here, $V_s = h(1.5\nu_0 - \nu_0)/e = 0.5h\nu_0/e$ .

Now intensity is doubled. Intensity affects the number of photons per second — which changes the current (and hence saturation current), but not the energy of individual photons.

Since stopping potential depends only on photon energy and work function, $V_s$ stays the same.

Answer: (B)

The most common wrong answer here is (A). Students confuse intensity with frequency. More intensity = more electrons emitted = higher current. But stopping potential is about the energy of the fastest electron, which doesn’t change when you add more photons of the same energy.

PYQ 2 — Bohr Model (JEE Main 2022, Shift 2)

Question: An electron in hydrogen atom jumps from $n=4$ to $n=2$ . The wavelength of emitted radiation falls in which series? Also find the energy of the photon emitted.

Solution:

Balmer series corresponds to transitions ending at $n=2$ . A jump from $n=4$ to $n=2$ ends at $n=2$ , so this is the Balmer series (visible light region).

Energy of photon:

\Delta E = 13.6\left(\frac{1}{2^2} - \frac{1}{4^2}\right) = 13.6\left(\frac{1}{4} - \frac{1}{16}\right)

= 13.6 \times \frac{3}{16} = 13.6 \times 0.1875 = 2.55 \text{ eV}

Answer: Balmer series, 2.55 eV

Memorise the series boundaries: Lyman ends at $n=1$ (UV), Balmer at $n=2$ (visible), Paschen at $n=3$ (IR). The ending level determines the series — the starting level just determines which line within that series.

PYQ 3 — Radioactive Decay (JEE Main 2023, Shift 1)

Question: A radioactive substance has a half-life of 10 days. After 30 days, what fraction of the original substance remains? If we started with $6.4 \times 10^{20}$ atoms, how many atoms remain?

Solution:

30 days = 3 half-lives.

\frac{N}{N_0} = \left(\frac{1}{2}\right)^3 = \frac{1}{8}

Number of atoms remaining:

N = \frac{6.4 \times 10^{20}}{8} = 0.8 \times 10^{20} = 8 \times 10^{19} \text{ atoms}

Answer: 1/8 of original; $8 \times 10^{19}$ atoms

This is a straightforward PYQ but the numbers are chosen to catch students who miscount half-lives. Always verify: 10, 20, 30 days → 1st, 2nd, 3rd half-life.

Difficulty Distribution

Based on analysis of JEE Main papers from 2019–2024:

Difficulty	% of Questions	What It Tests
Easy	40%	Direct formula application — stopping potential, half-life, Bohr energy levels
Medium	45%	Two-step problems — combining photoelectric effect with energy conservation, successive decay
Hard	15%	Nuclear Q-value with mass-energy equivalence, hydrogen-like ions with multiple transitions

Most Modern Physics questions in JEE Main are Easy to Medium. This means a well-prepared student should be scoring full marks here — it’s not a chapter where you should lose points due to concept confusion. The hard questions are usually from nuclear physics; skip them in the exam if unsure and come back.

Expert Strategy

How toppers approach this chapter:

First, lock down the three core formulas — photoelectric equation, Bohr energy levels, and decay law. These three alone will solve 70% of questions you’ll ever see.

For Bohr model questions, build a mental map of the hydrogen energy levels. $E_1 = -13.6$ eV, $E_2 = -3.4$ eV, $E_3 = -1.51$ eV, $E_4 = -0.85$ eV. Memorising these saves 30–40 seconds per question, which adds up.

In JEE Main, radioactivity problems almost always involve “how much remains after $n$ half-lives” or “find the half-life given activity at two times.” The second type uses $A = A_0 e^{-\lambda t}$ and requires taking a logarithm. Practice both types until they’re automatic.

For nuclear physics, understand Q-value conceptually: $Q = (\text{mass of reactants} - \text{mass of products}) \times 931.5$ MeV/u. Positive Q means energy is released (exothermic). In JEE Advanced, you might need to compute this — keep atomic mass units (u) and the conversion factor handy.

In the exam, Modern Physics questions typically appear in the first half of the Physics section. Since they’re formula-heavy and less calculation-intensive than Mechanics or Electrostatics, many toppers solve these first to bank the marks and build confidence.

Time budget: Aim for 2–3 minutes per Modern Physics question in JEE Main. If a question crosses 4 minutes, mark it and move on.

Common Traps

Trap 1 — Confusing threshold frequency with threshold wavelength. Higher threshold frequency means higher work function. But higher threshold wavelength means lower work function (since $\phi = hc/\lambda_0$ ). Examiners routinely switch between frequency and wavelength in options to catch this.

Trap 2 — Hydrogen-like ion vs. hydrogen atom. For He⁺ ( $Z=2$ ), energy levels are $E_n = -13.6 \times 4/n^2$ eV. The ground state energy is $-54.4$ eV, not $-13.6$ eV. Whenever the problem says “hydrogen-like ion” or gives atomic number $Z > 1$ , multiply by $Z^2$ .

Trap 3 — Mean life vs. half-life. Mean life $\tau = T_{1/2}/0.693 = 1.44 \times T_{1/2}$ . So mean life is longer than half-life. Students often flip this. The mean life is the time for the substance to reduce to $1/e$ (≈ 37%) of its original amount — not 50%.

Trap 4 — Activity vs. number of atoms. Activity $A = \lambda N$ . If half the atoms remain, activity is also halved. But students sometimes think activity stays constant because “radioactivity is a property of the substance.” Activity drops as atoms are used up.

Trap 5 — de Broglie wavelength and relativistic electrons. The formula $\lambda = h/\sqrt{2meV}$ is valid only for non-relativistic particles. If the problem gives very high voltage (say, $V > 10^5$ V for electrons), relativistic corrections apply. JEE rarely tests this, but if options don’t match, check whether relativistic mass is being used.