iCON Education - Atoms and Nuclei JEE Advanced Test

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Student

Exam Name

JEE Advanced

Test Name

Atoms and Nuclei

Subject

Physics

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Question 1: Palette 1/43

JEE Advanced 2026 MCQ

A nuclear reactor starts producing a radioactive nuclide X from t = 0, at a constant rate of α per second. Each decay of X produces energy E₀, which is utilized to heat a liquid of mass m and specific heat s. Assuming no heat loss from the liquid and taking λ as the decay constant of X, the rate of increase in the temperature of the liquid is :

$ \frac{\alpha E_0}{ms} (1 - e^{-\lambda t}) $

$ \frac{\alpha E_0}{ms} (e^{\lambda t} - 1) $

$ \frac{\lambda E_0}{ms} (1 - e^{-\lambda t}) $

$ \frac{E_0}{ms} (\alpha - \lambda e^{-\lambda t}) $

Question 3: Palette 3/43

JEE Advanced 2025 MCQ

List-I shows various functional dependencies of energy $(E)$ on the atomic number $(Z)$. Energies associated with certain phenomena are given in List-II.

Choose the option that describes the correct match between the entries in List-I to those in List-II.

List–I	List–II
(P) $E \propto Z^2$	(1) energy of characteristic x-rays
(Q) $E \propto (Z - 1)^2$	(2) electrostatic part of the nuclear binding energy for stable nuclei with mass numbers in the range 30 to 170
(R) $E \propto Z(Z - 1)$	(3) energy of continuous x-rays
(S) $E$ is practically independent of $Z$	(4) average nuclear binding energy per nucleon for stable nuclei with mass number in the range 30 to 170
	(5) energy of radiation due to electronic transitions from hydrogen-like atoms

P→4, Q→3, R→1, S→2

P→5, Q→2, R→1, S→4

P→5, Q→1, R→2, S→4

P→3, Q→2, R→1, S→5

Question 4: Palette 4/43

JEE Advanced 2024 MSQ

A particle of mass $m$ is moving in a circular orbit under the influence of the central force $F(r)=-k r$, corresponding to the potential energy $V(r)=k r^2 / 2$, where $k$ is a positive force constant and $r$ is the radial distance from the origin. According to the Bohr's quantization rule, the angular momentum of the particle is given by $L=n \hbar$, where $\hbar=h /(2 \pi), h$ is the Planck's constant, and $n$ a positive integer. If $v$ and $E$ are the speed and total energy of the particle, respectively, then which of the following expression(s) is(are) correct?

$r^2=n \hbar \sqrt{\frac{1}{m k}}$

$v^2=n \hbar \sqrt{\frac{k}{m^3}}$

$\frac{L}{m r^2}=\sqrt{\frac{k}{m}}$

$E=\frac{n \hbar}{2} \sqrt{\frac{k}{m}}$

Question 5: Palette 5/43

JEE Advanced 2023 MCQ

List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option.

List - I	List - II
(P) ${ }_{92}^{238} U \rightarrow{ }_{91}^{234} \mathrm{~Pa}$	(1) one $\alpha$ particle and one $\beta^{+}$particle
(Q) ${ }_{82}^{214} \mathrm{~Pb} \rightarrow{ }_{82}^{210} \mathrm{~Pb}$	(2) three $\beta^{-}$particles and one $\alpha$ particle
(R) ${ }_{81}^{210} \mathrm{Tl} \rightarrow{ }_{82}^{206} \mathrm{~Pb}$	(3) two $\beta^{-}$particles and one $\alpha$ particle
(S) ${ }_{91}^{228} \mathrm{~Pa} \rightarrow{ }_{88}^{224} \mathrm{Ra}$	(4) one $\alpha$ particle and one $\beta^{-}$particle
	(5) one $\alpha$ particle and two $\beta^{+}$particles

$P \rightarrow 4, Q \rightarrow 3, R \rightarrow 2, S \rightarrow 1$

$P \rightarrow 4, Q \rightarrow 1, R \rightarrow 2, S \rightarrow 5$

$P \rightarrow 5, Q \rightarrow 3, R \rightarrow 1, S \rightarrow 4$

$P \rightarrow 5, Q \rightarrow 1, R \rightarrow 3, S \rightarrow 2$

Question 6: Palette 6/43

JEE Advanced 2022 MSQ

The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be $E_{b}^{p}$ and the binding energy of a neutron be $E_{b}^{n}$ in the nucleus.

Which of the following statement(s) is(are) correct?

$E_{b}^{p}-E_{b}^{n}$ is proportional to $Z(Z-1)$ where $Z$ is the atomic number of the nucleus.

$E_{b}^{p}-E_{b}^{n}$ is proportional to $A^{-\frac{1}{3}}$ where $A$ is the mass number of the nucleus.

$E_{b}^{p}-E_{b}^{n}$ is positive.

$E_{b}^{p}$ increases if the nucleus undergoes a beta decay emitting a positron.

Question 7: Palette 7/43

JEE Advanced 2021 MCQ

A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decays of Q in the first one hour is

350

525

Question 10: Palette 10/43

JEE Advanced 2020 MSQ

In an X-ray tube, electrons emitted from a filament (cathode) carrying current I hit a target (anode) at a distance d from the cathode. The target is kept at a potential V higher than the cathode resulting in emission of continuous and characteristic X-rays. If the filament current I is decreased to ${1 \over 2}$, the potential difference V is increased to 2V, and the separation distance d is reduced to ${d \over 2}$, then

the cut-off wavelength will reduce to half, and the wavelengths of the characteristic X-rays will remain the same

the cut-off wavelength as well as the wavelengths of the characteristic X-rays will remain the same

the cut-off wavelength will reduce to half, and the intensities of all the X-rays will decrease

the cut-off wavelength will become two times larger, and the intensity of all the X-rays will decrease

Question 12: Palette 12/43

JEE Advanced 2019 MCQ

In a radioactive sample, ${}_{19}^{40}K$ nuclei either decay into stable ${}_{20}^{40}Ca$ nuclei with decay constant 4.5 $ \times $ 10^-10 per year or into stable ${}_{18}^{40}Ar$ nuclei with decay constant 0.5 $ \times $ 10^-10 per year. Given that in this sample all the stable ${}_{20}^{40}Ca$ and ${}_{18}^{40}Ar$ nuclei are produced by the ${}_{19}^{40}K$ nuclei only. In time t $ \times $ 10⁹ years, if the ratio of the sum of stable ${}_{20}^{40}Ca$ and ${}_{18}^{40}Ar$ nuclei to the radioactive ${}_{19}^{40}K$ nuclei is 99, the value of t will be

[Given : In 10 = 2.3]

9.2

1.15

4.6

2.3

Question 14: Palette 14/43

JEE Advanced 2018 MSQ

In a radioactive decay chain, ${}_{90}^{232}Th$ nucleus decays to ${}_{82}^{212}Pb$ nucleus. Let ${N_\alpha }$ and ${N_\beta }$ be the number of $\alpha $ and ${\beta ^ - }$ particles, respectively, emitted in this decay process. Which of the following statements is (are) true?

${N_\alpha } = 5$

${N_\alpha } = 6$

${N_\beta } = 2$

${N_\beta } = 4$

Question 15: Palette 15/43

JEE Advanced 2016 MCQ

An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?

108

120

Question 17: Palette 17/43

JEE Advanced 2016 MSQ

Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principle quantum number n, where n >> 1. Which of the following statement(s) is(are) true?

Relative change in the radii of two consecutive orbitals does not depend on Z.

Relative change in the radii of two consecutive orbitals varies as 1/n

Relative change in the energy of two consecutive orbitals varies as 1/n³

Relative change in the angular momenta of two consecutive orbitals varies as 1/n

Question 18: Palette 18/43

JEE Advanced 2015 MCQ

Match the nuclear processes given in Column I with the appropriate option(s) in Column II:

JEE Advanced 2015 Paper 1 Offline Physics - Atoms and Nuclei Question 37 English

(A)→(R) or (RT), (T); (B)→(P), (S); (C)→(Q), (T); (D)→(R)

(A)→(R), (T); (B)→(Q), (S); (C)→(Q), (T); (D)→(R)

(A)→(R) or (RT), (T); (B)→(P), (S); (C)→(S), (T); (D)→(R)

(A)→(P), (T); (B)→(P), (S); (C)→(Q), (T); (D)→(R)

Question 19: Palette 19/43

JEE Advanced 2015 MCQ

A fission reaction is given by $_{92}^{236}U \to _{54}^{140}Xe + _{38}^{94}Sr + x + y$, where x and y are two particles. Considering $_{92}^{236}U$ to be at rest, the kinetic energies of the products are denoted by ${K_{Xe}},{K_{Sr}},{K_x}(2MeV)$ $ \text { and } \mathrm{K}_{\mathrm{y}}(2 \mathrm{MeV}) $, respectively. Let the binding energies per nucleon of $_{92}^{236}U$, $_{54}^{140}Xe$ and $_{38}^{94}Sr$ be 7.5 MeV, 8.5 MeV and 8.5 MeV, respectively. Considering different conservation laws, the correct options is/are

x = n, y = n, K_sr = 129 MeV, K_Xe = 86 MeV

x = p, y = e^$-$, K_sr = 129 MeV, K_Xe = 86 MeV

x = p, y = n, K_sr = 129 MeV, K_Xe = 86 MeV

x = n, y = n, K_sr = 86 MeV, K_Xe = 129 MeV

Question 20: Palette 20/43

JEE Advanced 2014 MCQ

If $\lambda$_Cu is the wavelength of K_$\alpha$ X-ray line of copper (atomic number 29) and $\lambda$_Mo is the wavelength of the K_$\alpha$ X-ray line of molybdenum (atomic number 42), then the ratio $\lambda$_Cu/$\lambda$_Mo is close to

1.99

2.14

0.50

0.48

Question 21: Palette 21/43

JEE Advanced 2013 MCQ

The correct statement is

the nucleus $_3^6Li$ can emit an alpha particle.

the nucleus $_{84}^{210}Po$ can emit a proton.

deuteron and alpha particle can undergo complete fusion.

the nuclei $_{30}^{70}Zn$ and $_{34}^{82}Se$ can undergo complete fusion.

Question 22: Palette 22/43

JEE Advanced 2013 MCQ

The kinetic energy (in keV) of the alpha particle, when the nucleus $_{84}^{210}Po$ at rest undergoes alpha decay, is

5319

5422

5707

5818

Question 23: Palette 23/43

JEE Advanced 2013 MCQ

Match List I of the nuclear processes with List II containing parent nucleus and one of the end products of each process and then select the correct answer using the codes given below the lists :

	List I		List II
P.	Alpha decay	1.	$_8^{15}O \to _7^{15}N + ...$
Q.	${\beta ^ + }$ decay	2.	$_{91}^{238}U \to _{90}^{234}Th + ...$
R.	Fission	3.	$_{83}^{185}Bi \to _{82}^{184}Pb + ...$
S.	Proton emission	4.	$_{94}^{239}Pu \to _{57}^{140}La + ...$

P-4, Q-2, R-1, S-3

P-1, Q-3, R-2, S-4

P-2, Q-1, R-4, S-3

P-4, Q-3, R-2, S-1

Question 25: Palette 25/43

JEE Advanced 2012 MCQ

What is the maximum energy of the anti-neutrino?

Zero.

Much less than 0.8 $\times$ 10⁶ eV.

Nearly 0.8 $\times$ 10⁶ eV.

much larger than 0.8 $\times$ 10⁶ eV.

Question 26: Palette 26/43

JEE Advanced 2012 MCQ

If the anti-neutrino had a mass of 3 eV/c² (where c is the speed of light) instead of zero mass, what should be the range of the kinetic energy, K, of the electron?

0 $\le$ K $\le$ 0.8 $\times$ 10⁶ eV

3.0 eV $\le$ K $\le$ 0.8 $\times$ 10⁶ eV

3.0 eV $\le$ K < 0.8 $\times$ 10⁶ eV

0 $\le$ K < 0.8 $\times$ 10⁶ eV

Question 27: Palette 27/43

JEE Advanced 2011 MCQ

The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 $\mathop A\limits^o $. The wavelength of the second spectral line in the Balmer series of singly-ionized helium atom is

1215 $\mathop A\limits^o $

1640 $\mathop A\limits^o $

2430 $\mathop A\limits^o $

4687 $\mathop A\limits^o $

Question 29: Palette 29/43

JEE Advanced 2010 MCQ

It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule is close to ${4 \over \pi } \times {10^{11}}$ Hz. Then, the moment of inertia of CO molecule about its centre of mass is close to (Take h = 2$\pi$ $\times$ 10^$-$34 J-s)

2.76 $\times$ 10^$-$46 kg m²

1.87 $\times$ 10^$-$46 kg m²

4.67 $\times$ 10^$-$47 kg m²

1.17 $\times$ 10^$-$47 kg m²

Question 30: Palette 30/43

JEE Advanced 2010 MCQ

In a CO molecule, the distance between C (mass = 12 amu) and O (mass = 16 amu), where 1 amu $ = {5 \over 3} \times {10^{ - 27}}$ kg, is close to :

2.4 $\times$ 10^$-$10 m

1.9 $\times$ 10^$-$10 m

1.3 $\times$ 10^$-$10 m

4.4 $\times$ 10^$-$11 m

Question 31: Palette 31/43

JEE Advanced 2009 MCQ

The speed of the particle, that can take discrete values, is proportional to

${n^{ - 3/2}}$

${n^{ - 1}}$

${n^{1/2}}$

$n$

Question 32: Palette 32/43

JEE Advanced 2009 MCQ

In the core of nuclear fusion reactor, the gas becomes plasma because of

strong nuclear force acting between the deuterons.

Coulomb force acting between the deuterons.

Coulomb force acting between deuteron-electrons pairs.

the high temperature maintained inside the reactor core.

Question 33: Palette 33/43

JEE Advanced 2009 MCQ

Assume that two deuteron nuclei in the core of fusion reactor at temperature T are moving towards each other, each with kinetic energy 1.5 kT, when the separation between them is large enough to neglect Coulomb potential energy. Also neglect any interaction from other particles in the core. The minimum temperature T required for them to reach a separation of 4 $\times$ 10$^{-15}$ m is in the range

$1.0 \times {10^9}K < T < 2.0 < {10^9}K$

$2.0 \times {10^9}K < T < 3.0 < {10^9}K$

$3.0 \times {10^9}K < T < 4.0 < {10^9}K$

$4.0 \times {10^9}K < T < 5.0 < {10^9}K$

Question 34: Palette 34/43

JEE Advanced 2009 MCQ

Results of calculations for four different designs of a fusion reactor using D-D reaction are given below. Which of these is most promising based on Lawson criterion?

Deuteron density = $2.0\times10^{12}~\mathrm{cm^{-3}}$; Confinement time = $5.0\times10^{-3}~\mathrm{s}$.

Deuteron density = $8.0\times10^{14}~\mathrm{cm^{-3}}$; Confinement time = $9.0\times10^{-1}~\mathrm{s}$.

Deuteron density = $4.0\times10^{23}~\mathrm{cm^{-3}}$; Confinement time = $1.0\times10^{-11}~\mathrm{s}$.

Deuteron density = $1.0\times10^{24}~\mathrm{cm^{-3}}$; Confinement time = $4.0\times10^{-12}~\mathrm{s}$.

Question 35: Palette 35/43

JEE Advanced 2008 MCQ

A radioactive sample S₁ having activity of 5 $\mu$Ci has twice the number of nuclei as another sample S₂ which has an activity of 10 $\mu$Ci. The half lives of S₁ and S₂ can be :

20 years and 5 years, respectively

20 years and 10 years, respectively

10 years each

5 years each

Question 36: Palette 36/43

JEE Advanced 2008 MCQ

The quantum number n of the state finally populated in He$^+$ ions is :

Question 37: Palette 37/43

JEE Advanced 2008 MCQ

The wavelength of light emitted in the visible region by He$^+$ ions after collisions with H atoms is

$6.5\times10^{-7}$ m

$5.6\times10^{-7}$ m

$4.8\times10^{-7}$ m

$4.0\times10^{-7}$ m

Question 38: Palette 38/43

JEE Advanced 2008 MCQ

The ratio of the kinetic energy of the $n=2$ electron for the H atom to that of He$^+$ ion is

$\frac{1}{4}$

$\frac{1}{2}$

Question 39: Palette 39/43

JEE Advanced 2008 MSQ

Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the figure. Use this plot to choose the correct choice(s) given below.

IIT-JEE 2008 Paper 1 Offline Physics - Atoms and Nuclei Question 14 English

Fusion of two nuclei with mass number lying in the range of 1 < A < 50 will release energy

Fusion of two nuclei with mass numbers lying in the range of 51 < A < 100 will release energy

Fission of a nucleus lying in the mass range of 100 < A < 200 will release energy when broken into two equal fragments

Fission of a nucleus lying in the mass range of 200 < A < 260 will release energy when broken into two equal fragments

Question 40: Palette 40/43

JEE Advanced 2007 MCQ

In the option given below, let E denote the rest mass energy of a nucleus and n a neutron. The correct option is

$E\left( {_{92}^{236}U} \right) > E\left( {_{53}^{137}I} \right) + E\left( {_{39}^{97}Y} \right) + 2E(n)$

$E\left( {_{92}^{236}U} \right) < E\left( {_{53}^{137}I} \right) + E\left( {_{39}^{97}Y} \right) + 2E(n)$

$E\left( {_{92}^{236}U} \right) < E\left( {_{56}^{140}Ba} \right) + E\left( {_{36}^{94}Kr} \right) + 2E(n)$

$E\left( {_{92}^{236}U} \right) = E\left( {_{56}^{140}Ba} \right) + E\left( {_{36}^{94}Kr} \right) + 2E(n)$

Question 41: Palette 41/43

JEE Advanced 2007 MCQ

The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is

802 nm

823 nm

1882 nm

1648 nm

Question 42: Palette 42/43

JEE Advanced 2006 MCQ

$ \text { Match the following Columns. } $

Column I		Column II
(A)	Nuclear fusion.	(P)	Converts some matter into energy.
(B)	Nuclear fission.	(Q)	Generally possible for nuclei with low atomic number.
(C)	$\beta$-decay.	(R)	Generally possible for nuclei with higher atomic number.
(D)	Exothermic nuclear reaction.	(S)	Essentially proceeds by weak nuclear forces.

$ [\mathrm{A} \rightarrow( \mathrm{Q}) ; \mathrm{B} \rightarrow(\mathrm{P}, \mathrm{R}) ; \mathrm{C} \rightarrow(\mathbf{P}, \mathbf{S}) ; \mathbf{D} \rightarrow( \mathbf{R})] $

$ [\mathrm{A} \rightarrow(\mathrm{P}) ; \mathrm{B} \rightarrow(\mathrm{P}, \mathrm{R}) ; \mathrm{C} \rightarrow(\mathbf{P}) ; \mathbf{D} \rightarrow(\mathbf{P}, \mathbf{Q}, \mathbf{R})] . $

$ [\mathrm{A} \rightarrow(\mathrm{P}, \mathrm{Q}) ; \mathrm{B} \rightarrow(\mathrm{P}, \mathrm{R}) ; \mathrm{C} \rightarrow(\mathbf{P}, \mathbf{S}) ; \mathbf{D} \rightarrow(\mathbf{P}, \mathbf{Q}, \mathbf{R})] . $

$ [\mathrm{A} \rightarrow(\mathrm{P}, \mathrm{Q}) ; \mathrm{B} \rightarrow(\mathrm{P}, \mathrm{R}) ; \mathrm{C} \rightarrow( \mathbf{S}) ; \mathbf{D} \rightarrow(\mathbf{P}, \mathbf{Q})] . $

Question 43: Palette 43/43

JEE Advanced 2005 MCQ

Highly energetic electrons are bombarded on a target of an element containing 30 neutrons. The ratio of radii of nucleus to that of Helium nucleus is $(14)^{\frac{1}{3}}$. Find

(A) Atomic number of the nucleus;

(B) the frequency of $\mathrm{K}_{\alpha}$ line of the X-ray produced.

$\left(\mathrm{R}=1.1 \times 10^{7} \mathrm{~m}^{-1}\right.$ and $\left.c=3 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)$

(A) 26 ; (B) $2.55 \times 10^{18} \mathrm{~Hz}$

(A) 26 ; (B) $1.55 \times 10^{18} \mathrm{~Hz}$

(A) 36 ; (B) $1.55 \times 10^{18} \mathrm{~Hz}$

(A) 46 ; (B) $2.55 \times 10^{18} \mathrm{~Hz}$

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