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JEE Main · Physics · Class 12
Modern physics — dual nature of matter and radiation together with atoms and nuclei — carries about two to four of the 25 JEE Main Physics questions in our reading of past papers. It is the highest-return block in the paper because the questions are short, formula-driven and repeat their patterns year after year.
Quick answer
Questions per paper
2–4
Dual nature plus atoms and nuclei
Marks at stake
8–16
At +4 / −1 per question
Difficulty
Easy–moderate
Short questions, high return
Class
12
Little dependence on Class 11 mechanics
BrainStride analysis of past papers
A photon of frequency f carries E = hf = hc/λ. With hc = 1240 eV·nm, a 400 nm photon carries 3.1 eV. Working in electron-volts and nanometres avoids most of the arithmetic slips in this chapter.
Electrons are emitted only above the threshold frequency, whatever the intensity. K_max = hf − φ, and the stopping potential satisfies eV₀ = hf − φ. Intensity controls how many electrons come out — the saturation current — not how fast they travel.
Every particle has λ = h/p = h/√(2mK). For an electron accelerated through a potential V, this reduces to λ ≈ 12.27/√V in ångströms with V in volts, which is the form the exam usually wants.
For a hydrogen-like atom, r_n = 0.529 n²/Z Å and E_n = −13.6 Z²/n² eV. Energy is negative because the electron is bound; the difference between two levels is what appears as a photon.
The emitted wavelength follows 1/λ = RZ²(1/n₁² − 1/n₂²) with n₁ < n₂. Lyman ends at n = 1 and lies in the ultraviolet; Balmer ends at n = 2 and gives the visible lines, of which n = 3 → 2 is the familiar 656 nm red.
Mass defect converts to binding energy through E = Δm c², with 1 u = 931.5 MeV. Binding energy per nucleon peaks near A = 56, which is why both fusion of light nuclei and fission of heavy ones release energy. Decay is exponential: N = N₀e^(−λt).
E = hf = hc/λ · hc = 1240 eV·nm
λ in nm gives E directly in eV.
K_max = hf − φ · eV₀ = hf − φ
V₀ is the stopping potential.
λ₀ = hc/φ
No emission for λ > λ₀, however intense the light.
λ = h/p = h/√(2mK) · λ(Å) ≈ 12.27/√V
The second form is for an electron accelerated through V volts.
r_n = 0.529 n²/Z Å · E_n = −13.6 Z²/n² eV
Hydrogen-like species only (one electron).
1/λ = R Z² (1/n₁² − 1/n₂²) · R = 1.097 × 10⁷ m⁻¹
n₁ is the lower level.
N = N₀ e^(−λt) · A = λN
Activity falls with the same exponential as the number of nuclei.
t½ = 0.693/λ · τ = 1/λ = t½/0.693
After n half-lives, the fraction left is (1/2)ⁿ.
E = Δm c² · 1 u = 931.5 MeV/c²
Mass defect Δm gives the binding energy.
R = R₀ A^(1/3) · R₀ ≈ 1.2 fm
Density is therefore nearly the same for all nuclei.
Why it happens
Constants are memorised in SI, but the questions are set in eV and nm.The fix
Work in eV and nm with hc = 1240 eV·nm throughout, and convert only if the answer options are in joules.Why it happens
Brighter light feels like more energetic light.The fix
Intensity changes the number of photons, so it changes the current. Only frequency changes the energy per photon, and therefore V₀.Why it happens
E_n = −13.6 Z²/n² looks general because it contains Z.The fix
It holds only for one-electron species — H, He⁺, Li²⁺. For anything else the electron–electron repulsion breaks the model.Why it happens
Both are quoted in MeV and the wording is close.The fix
Divide the total binding energy by A before comparing stability. The per-nucleon curve peaks near A = 56; the total keeps rising with A.Why it happens
Both describe how fast a sample decays and differ by a factor most students do not store.The fix
Write τ = 1/λ and t½ = 0.693/λ side by side, so τ = t½/0.693 ≈ 1.44 t½.6 questions
Question 1
The stopping potential in a photoelectric experiment depends on:
Question 2
Light of wavelength 400 nm falls on a metal of work function 2.0 eV. The maximum kinetic energy of the emitted electrons is:
Question 3
An electron is accelerated from rest through 100 V. Its de Broglie wavelength is about:
Question 4
The energy of the electron in the n = 2 level of a hydrogen atom is:
Question 5
A radioactive sample has an activity of 800 Bq and a half-life of 10 days. Its activity after 30 days is:
Question 6
Binding energy per nucleon is greatest for nuclei with mass number near:
A test on one chapter alone tells you little — the exam never asks Modern Physics in isolation. So this builds a full JEE Main Physics paper that leans on it. Weighted like the exam, a 25-question paper gives Modern Physics 2 questions; marked weak, it gets 5, and the rest of the paper keeps the other chapters honest. Fill the plan from previous-year questions or your module.
Your paper
Press Generate paper plan for a chapter-by-chapter blueprint: questions per chapter, numericals, marks and time — ready to print and fill from your PYQs, modules or the BrainStride question bank.
Chapter weights are BrainStride’s reading of past papers, not official data. For any other chapter mix, use the JEE Main Physics test generator.
Photoelectric effect · 3 marks · easy
The threshold wavelength for a metal is 600 nm. Light of wavelength 400 nm falls on it. Find the work function of the metal and the stopping potential.
Answer: φ ≈ 2.07 eV; V₀ ≈ 1.03 V.
Bohr model and spectra · 3 marks · easy
An electron in a hydrogen atom falls from n = 3 to n = 2. Find the energy of the emitted photon and its wavelength.
Answer: E ≈ 1.89 eV; λ ≈ 656 nm (visible red).
Nuclear decay · 3 marks · moderate
A radioactive nuclide has a half-life of 8 hours. What fraction of an initial sample remains after 24 hours, and what is its decay constant?
Answer: One-eighth of the sample remains; λ ≈ 0.087 h⁻¹ (2.4 × 10⁻⁵ s⁻¹).
In BrainStride’s analysis of past JEE Main papers, dual nature of matter and radiation together with atoms and nuclei account for about two to four of the 25 Physics questions, and electronic devices can add one or two more. NTA publishes no official chapter weightage, so treat these as past-paper ranges.
It is among the highest-return chapters. Modern physics questions are usually one or two steps long, lean on a small set of formulas, and rarely hide the concept being tested. A student short of time typically gains more from finishing modern physics than from another week on rotational mechanics.
hc = 1240 eV·nm. With it, the energy of any photon in electron-volts is simply 1240 divided by the wavelength in nanometres, which turns photoelectric and spectral questions into one line of arithmetic and removes most of the unit conversion errors.
No. The Bohr formulas r_n = 0.529 n²/Z Å and E_n = −13.6 Z²/n² eV hold only for hydrogen-like species with a single electron, such as H, He⁺ and Li²⁺. Applying them to neutral helium or lithium is a common and easily avoided error.
Half-life t½ = 0.693/λ is the time for half the nuclei to decay. Mean life τ = 1/λ is the average lifetime of a nucleus and is longer, τ ≈ 1.44 t½. Questions often supply one and ask for the other, so store both alongside the decay constant.
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