How much of JEE Main comes from Modern Physics?

JEEGenie estimates about 6% of JEE Main marks come from Modern Physics, based on recent papers. The share varies from year to year.

Which formulas matter most in Modern Physics?

The Modern Physics sheet on this page has 23 formula entries, starting with Photoelectric Effect, Einstein's Photoelectric Equation, Work Function and Threshold Frequency, Stopping Potential Calculation, de Broglie Wavelength. Each one comes with when to use it and the trap to avoid.

What topics does Modern Physics cover for JEE?

Modern Physics covers Photoelectric Effect, Bohr Model and Atomic Spectra, Matter Waves, Nuclear Physics, Radioactivity, Semiconductor Devices.

How should I revise Modern Physics before the exam?

Learn each formula together with its condition of use, read the trap listed beside it, then practise questions and review every mistake. The practice link on this page opens Modern Physics questions on JEEGenie.

How many previous-year questions are there on Modern Physics?

JEEGenie has 947 previous-year questions on Modern Physics, and this page shows a few with worked explanations.

Is practice on Modern Physics free on JEEGenie?

Sign-up is free and includes a 7-day Pro trial. After the trial, free accounts keep a limited daily quota.

Modern Physics for JEE Main & Advanced — formulas, what is asked, and traps

JEEGenie estimates about 6% of JEE Main marks come from Modern Physics. This page covers 23 formula entries, each with when to use it, what JEE asks and the traps. A common slip: Confusing intensity with frequency: intensity affects number of photoelectrons, not their maximum kinetic energy.

Key points to know

Photoelectric Effect. Emission of electrons from a metal surface when light of sufficient frequency (above threshold) strikes it.
Work Function and Threshold Frequency. Minimum energy needed to eject an electron from a metal; threshold frequency $ν_{0} = ϕ / h$ .
de Broglie Wavelength. Every moving particle has a wavelength associated with it, inversely proportional to its momentum.
Bohr's Model of Hydrogen Atom. Electrons orbit nucleus in quantized energy levels; angular momentum is $n ℏ$ .
Nuclear Binding Energy. Energy required to break a nucleus into its constituent protons and neutrons; mass defect converted to energy.
Mass-Energy Equivalence. Mass and energy are interchangeable; a small mass corresponds to a huge amount of energy.
Compton Effect. Scattering of X-rays by electrons results in increase in wavelength (Compton shift).
Nuclear Fission and Fusion. Fission: heavy nucleus splits into lighter ones, releasing energy. Fusion: light nuclei combine to form heavier, releasing energy.
Photoelectric Effect: Saturation Current. Maximum photocurrent when all emitted electrons reach anode; proportional to light intensity.
Mean Life of Radioactive Nucleus. Average lifetime of a radioactive nucleus before decay; reciprocal of decay constant.

Formula sheet

Name	Formula	When to use
Photoelectric Effect	$E = h ν = ϕ + K_{max}$	When analyzing light-induced electron emission, calculating stopping potential, or threshold frequency.
Einstein's Photoelectric Equation	$h ν = ϕ + \frac{1}{2} m v_{max}^{2}$	To relate photon energy, work function, and electron kinetic energy in photoelectric problems.
Work Function and Threshold Frequency	$ϕ = h ν_{0} = \frac{h c}{λ_{0}}$	To determine if photoelectric emission occurs for a given wavelength/frequency.
Stopping Potential Calculation	$V_{0} = \frac{h ν - ϕ}{e}$	When given stopping potential data to find $h$ , $ϕ$ , or $K_{max}$ .
de Broglie Wavelength	$λ = \frac{h}{p} = \frac{h}{m v}$	When calculating wavelength of electrons, protons, or other particles in motion.
de Broglie Wavelength for Accelerated Electron	$λ = \frac{h}{\sqrt{2 m e V}}$	When an electron is accelerated by a voltage, e.g., in electron microscopes or diffraction experiments.
Bohr's Model of Hydrogen Atom	$L = m v r = n ℏ$ , $E_{n} = - \frac{13.6}{n^{2}} eV$	For hydrogen-like atoms (single electron) to find energy levels, radii, or transition wavelengths.
Rydberg Formula for Hydrogen Spectrum	$\frac{1}{λ} = R_{H} (\frac{1}{n_{f}^{2}} - \frac{1}{n_{i}^{2}})$	To find wavelengths of spectral lines in hydrogen (Lyman, Balmer, Paschen series).
Nuclear Binding Energy	$Δ m = [Z m_{p} + (A - Z) m_{n}] - M_{nucleus}$ , $B . E . = Δ m c^{2}$	To compare stability of nuclei; higher binding energy per nucleon means more stable.
Radioactive Decay Law	$N = N_{0} e^{- λ t}$ , $λ = \frac{\ln 2}{T_{1 / 2}}$	To find remaining nuclei after time $t$ , or half-life from decay data.
Solving Decay Problems with Half-Life	$N = N_{0} {(\frac{1}{2})}^{t / T_{1 / 2}}$	Quick calculation when time is multiple of half-life; otherwise use $N = N_{0} e^{- λ t}$ .
Mass-Energy Equivalence	$E = m c^{2}$	In nuclear reactions, to find energy released from mass defect.
Energy of a Photon	$E = h ν = \frac{h c}{λ}$	To find energy of a photon given frequency or wavelength.
Compton Effect	$Δ λ = λ^{'} - λ = \frac{h}{m_{e} c} (1 - \cos θ)$	When X-rays or gamma rays scatter off electrons, causing wavelength change.
Identifying Spectral Series in Hydrogen	Lyman: $n_{i} \geq 2 \to n_{f} = 1$ ; Balmer: $n_{i} \geq 3 \to n_{f} = 2$ ; Paschen: $n_{i} \geq 4 \to n_{f} = 3$	To classify spectral lines of hydrogen based on lower energy level.
Nuclear Fission and Fusion	Fission: $_{92}^{235} U + n \to fission fragments + 2 - 3 n + energy$	In nuclear energy problems, chain reactions, or stellar energy.
Bohr Radius and Energy for Hydrogen-like Atoms	$r_{n} = \frac{n^{2} a_{0}}{Z}$ , $E_{n} = - \frac{13.6 Z^{2}}{n^{2}} eV$	For ions like He $^{+}$ , Li $^{2 +}$ to find energy levels or radii.
Using Activity and Half-Life in Decay Problems	$A = A_{0} e^{- λ t}$ , $λ = \frac{\ln 2}{T_{1 / 2}}$	To find activity after time $t$ , or to determine half-life from activity measurements.
Photoelectric Effect: Saturation Current	$I_{sat} \propto intensity$	When analyzing how photocurrent varies with intensity or applied voltage.
Momentum of a Photon	$p = \frac{h}{λ} = \frac{E}{c}$	In radiation pressure problems, or Compton effect calculations.
Solving for Wavelength in Hydrogen Transitions	$\frac{1}{λ_{limit}} = R_{H} (\frac{1}{n_{f}^{2}})$	To find the boundary wavelength of a spectral series.
Mean Life of Radioactive Nucleus	$τ = \frac{1}{λ} = \frac{T_{1 / 2}}{\ln 2}$	When given mean life to find decay constant or half-life.
Energy Released in Nuclear Reactions	$Q = (m_{initial} - m_{final}) c^{2}$	To find energy released or absorbed in any nuclear reaction.

Open the Modern Physics formula page

What JEE asks

Photoelectric Effect. JEE often asks to find $K_{max}$ or $V_{0}$ given wavelength/frequency, or to interpret graphs of $K_{max}$ vs $ν$ .
Einstein's Photoelectric Equation. JEE may give stopping potential data to find $ϕ$ or $h$ via slope of $V_{0}$ vs $ν$ graph.
Work Function and Threshold Frequency. JEE often asks to compute $ϕ$ from given $ν_{0}$ or $λ_{0}$ , or vice versa.
Stopping Potential Calculation. JEE may give a graph of $V_{0}$ vs $ν$ ; slope gives $h / e$ , intercept gives $- ϕ / e$ .
de Broglie Wavelength. JEE often asks for $λ$ of an electron accelerated through a potential $V$ : $λ = h / \sqrt{2 m e V}$ .
de Broglie Wavelength for Accelerated Electron. JEE may ask for $λ$ given $V$ , or find $V$ for a given $λ$ .
Bohr's Model of Hydrogen Atom. JEE often asks for energy of a given level, or wavelength of transition using Rydberg formula.
Rydberg Formula for Hydrogen Spectrum. JEE may ask to identify series (e.g., Balmer for visible) or compute $λ$ for a transition.
Nuclear Binding Energy. JEE may give mass defect in amu and ask for B.E. in MeV (1 amu = 931.5 MeV/c $^{2}$ ).
Radioactive Decay Law. JEE often asks for fraction remaining after $n$ half-lives: $N / N_{0} = (1 / 2)^{n}$ .
Solving Decay Problems with Half-Life. JEE may give a graph of activity vs time to find half-life.
Mass-Energy Equivalence. JEE often asks to compute energy released in fission/fusion given mass difference in amu.
Energy of a Photon. JEE may ask for number of photons in a beam of given power and wavelength.
Compton Effect. JEE may ask for $Δ λ$ given angle, or find angle from shift.
Identifying Spectral Series in Hydrogen. JEE may ask to identify which series a given wavelength belongs to.
Nuclear Fission and Fusion. JEE may ask to calculate energy released from a given fission/fusion reaction using mass defect.
Bohr Radius and Energy for Hydrogen-like Atoms. JEE may ask for ionization energy of He $^{+}$ (54.4 eV) or radius of Li $^{2 +}$ .
Using Activity and Half-Life in Decay Problems. JEE may give initial activity and half-life to find activity after a given time.
Photoelectric Effect: Saturation Current. JEE may show I-V curves for different intensities and ask to identify saturation current.
Momentum of a Photon. JEE may ask for momentum transfer when photon is absorbed or reflected.
Solving for Wavelength in Hydrogen Transitions. JEE may ask for the shortest wavelength in Lyman or Balmer series.
Mean Life of Radioactive Nucleus. JEE may ask to compute $τ$ from $λ$ or vice versa.
Energy Released in Nuclear Reactions. JEE often gives masses in amu and asks for Q-value in MeV.

Common traps

Confusing intensity with frequency: intensity affects number of photoelectrons, not their maximum kinetic energy. Photoelectric Effect
Using $ν$ (frequency) instead of $f$ ; both are same but be consistent. Einstein's Photoelectric Equation
Assuming work function is same for all metals; it varies with material. Work Function and Threshold Frequency
Using $V_{0}$ as kinetic energy directly; it's potential difference, so multiply by $e$ . Stopping Potential Calculation
Applying to photons: $p = h / λ$ works, but $m = 0$ so $λ = h / p$ is consistent. de Broglie Wavelength
Using $m$ in kg, $e$ in C, $V$ in volts; result in meters. de Broglie Wavelength for Accelerated Electron
Assuming $n$ starts from 0; it starts from 1. Bohr's Model of Hydrogen Atom
Using $n_{i}$ and $n_{f}$ in wrong order; for emission $n_{i} > n_{f}$ . Rydberg Formula for Hydrogen Spectrum
Using atomic masses instead of nuclear masses; include electron masses carefully. Nuclear Binding Energy
Using $λ$ as decay constant; it's probability per unit time, not half-life. Radioactive Decay Law
Assuming $t / T_{1 / 2}$ must be integer; formula works for any real number. Solving Decay Problems with Half-Life
Using $c = 3 \times 10^{8} m/s$ ; energy in Joules if mass in kg. Mass-Energy Equivalence
Using $λ$ in nm but $h$ in J s; convert to meters. Energy of a Photon
Assuming shift depends on incident wavelength; it depends only on scattering angle. Compton Effect

Topics in Modern Physics

Photoelectric Effect
Bohr Model and Atomic Spectra
Matter Waves
Nuclear Physics
Radioactivity
Semiconductor Devices

Previous-year questions on Modern Physics

JEEGenie has 947 previous-year questions on Modern Physics. A few worked examples follow.

Year	Questions
2026	37
2025	43
2024	47
2023	78
2022	76
2021	106
2020	39
2019	123
2018	20
2017	20
2016	34
2015	19
2014	17
2013	29
2012	19
2011	7
2010	13
2009	14
2008	14
2007	9
2006	13
2005	12
2004	15
2003	16
2002	17
2001	7
2000	6
1999	8
1998	6
1997	10
1996	6
1995	1
1994	6
1993	3
1992	6
1991	2
1990	4
1989	5
1988	6
1987	4
1986	6
1985	4
1984	4
1983	7
1982	5
1981	4

Question 1 easy

For a certain metal, when monochromatic light of wavelength

λ

is incident, the stopping potential for photoelectrons is

3 V_{0}

. When the same metal is illuminated by light of wavelength

2 λ

, then the stopping potential becomes

V_{0}

. The threshold wavelength for photoelectric emission for the given metal is

α λ

. The value of

α

is ______.

Answer: B

Explanation. Einstein’s photoelectric equation:

\frac{h c}{λ} = \frac{h c}{λ_{0}} + e V_{s}

For wavelength

λ

, stopping potential

3 V_{0}

\begin{matrix} \frac{h c}{λ} = \frac{h c}{λ_{0}} + 3 e V_{0} & (1) \end{matrix}

For wavelength

2 λ

, stopping potential

V_{0}

\begin{matrix} \frac{h c}{2 λ} = \frac{h c}{λ_{0}} + e V_{0} & (2) \end{matrix}

Multiply (2) by 3:

\begin{matrix} \frac{3 h c}{2 λ} = \frac{3 h c}{λ_{0}} + 3 e V_{0} & (3) \end{matrix}

Subtract (1) from (3):

\frac{3 h c}{2 λ} - \frac{h c}{λ} = \frac{2 h c}{λ_{0}}

Simplify LHS:

\frac{3 h c - 2 h c}{2 λ} = \frac{h c}{2 λ}

So:

\frac{h c}{2 λ} = \frac{2 h c}{λ_{0}}

Cancel

h c

\frac{1}{2 λ} = \frac{2}{λ_{0}}

λ_{0} = 4 λ

Given

λ_{0} = α λ

, we get:

α = 4

B

From NTA/IIT papers: JEE Main 2026 · 2 Apr Shift 1

Question 2 medium

A zener diode with 5 V zener voltage is used to regulate an unregulated dc voltage input of 25 V . For a

400 Ω

resistor connected in series, the zener current is found to be 4 times load current. The load current

(I_{L})

and load resistance

(R_{L})

are :

$I_{L} = 0.02 m A; R_{L} = 250 Ω$
$I_{L} = 10 A; R_{L} = 0.5 Ω$
$I_{L} = 10 m A; R_{L} = 500 Ω$
$I_{L} = 20 m A; R_{L} = 250 Ω$

Answer: C

Explanation. Given:

V_{i n} = 25 V

V_{z} = 5 V

R_{s} = 400 Ω

, and

I_{z} = 4 I_{L}

. Voltage across

R_{s}

V_{R_{s}} = V_{i n} - V_{z} = 25 - 5 = 20 V

. Current through

R_{s}

I_{s} = \frac{V_{R_{s}}}{R_{s}} = \frac{20}{400} = 0.05 A = 50 m A

. Also,

I_{s} = I_{z} + I_{L} = 4 I_{L} + I_{L} = 5 I_{L}

. Thus

50 m A = 5 I_{L} \Rightarrow I_{L} = 10 m A

. Load resistance:

R_{L} = \frac{V_{z}}{I_{L}} = \frac{5}{0.01} = 500 Ω

. Thus the answer is option C.

From NTA/IIT papers: JEE Main 2025 · 2 Apr Shift 1

Question 3 hard

A metal target with atomic number

Z = 46

is bombarded with a high energy electron beam. The emission of X-rays from the target is analyzed. The ratio

r

of the wavelengths of the

K_{α}

-line and the cut-off is found to be

r = 2

. If the same electron beam bombards another metal target with

Z = 41

, the value of

r

will be

2.53
1.27
2.24
1.58

Answer: A

Explanation. For the

K_{α}

line, Moseley's law gives the frequency as

ν_{K_{α}} = c R (Z - 1)^{2} (\frac{1}{1^{2}} - \frac{1}{2^{2}}) = \frac{3 c R}{4} (Z - 1)^{2} .

Thus the wavelength of the

K_{α}

line is

λ_{K_{α}} = \frac{1}{ν_{K_{α}}} = \frac{4}{3 c R (Z - 1)^{2}} .

The cut-off wavelength depends only on the accelerating voltage

V

of the electron beam:

λ_{cut-off} = \frac{h c}{e V} .

Therefore the ratio is

r = \frac{λ_{K_{α}}}{λ_{cut-off}} = \frac{4}{3 c R (Z - 1)^{2}} \cdot \frac{e V}{h c} = \frac{4 e V}{3 h c^{2} R (Z - 1)^{2}} .

For the same electron beam,

V

is constant, so

r \propto \frac{1}{(Z - 1)^{2}} .

For

Z = 46

r = 2

. Hence for

Z = 41

r^{'} = r {(\frac{Z - 1}{Z^{'} - 1})}^{2} = 2 {(\frac{46 - 1}{41 - 1})}^{2} = 2 {(\frac{45}{40})}^{2} = 2 {(\frac{9}{8})}^{2} = 2 \cdot \frac{81}{64} = \frac{162}{64} = 2.53125.

Rounding to two decimal places gives

r^{'} \approx 2.53

. Answer: A

From NTA/IIT papers: JEE Advanced 2024

Question 4 hard

In a radioactive decay chain reaction,

_{90}^{230} Th

nucleus decays into

_{84}^{214} Po

nucleus. The ratio of the number of

α

to number of

β^{-}

particles emitted in this process is _____.

Answer: 2

Explanation. For each

α

-decay,

A

decreases by 4 and

Z

decreases by 2. For each

β^{-}

-decay,

A

unchanged and

Z

increases by 1. Let number of

α

particles be

x

and number of

β^{-}

particles be

y

. Mass number change:

230 - 4 x = 214 \Rightarrow 4 x = 16 \Rightarrow x = 4

. Atomic number change:

90 - 2 x + y = 84 \Rightarrow 90 - 8 + y = 84 \Rightarrow 82 + y = 84 \Rightarrow y = 2

. Thus ratio

\frac{x}{y} = \frac{4}{2} = 2

2

From NTA/IIT papers: JEE Advanced 2022

Frequently asked questions

How much of JEE Main comes from Modern Physics?: JEEGenie estimates about 6% of JEE Main marks come from Modern Physics, based on recent papers. The share varies from year to year.
Which formulas matter most in Modern Physics?: The Modern Physics sheet on this page has 23 formula entries, starting with Photoelectric Effect, Einstein's Photoelectric Equation, Work Function and Threshold Frequency, Stopping Potential Calculation, de Broglie Wavelength. Each one comes with when to use it and the trap to avoid.
What topics does Modern Physics cover for JEE?: Modern Physics covers Photoelectric Effect, Bohr Model and Atomic Spectra, Matter Waves, Nuclear Physics, Radioactivity, Semiconductor Devices.
How should I revise Modern Physics before the exam?: Learn each formula together with its condition of use, read the trap listed beside it, then practise questions and review every mistake. The practice link on this page opens Modern Physics questions on JEEGenie.
How many previous-year questions are there on Modern Physics?: JEEGenie has 947 previous-year questions on Modern Physics, and this page shows a few with worked explanations.
Is practice on Modern Physics free on JEEGenie?: Sign-up is free and includes a 7-day Pro trial. After the trial, free accounts keep a limited daily quota.