# Atoms and Nuclei · Physics · JEE Main

Start Practice## MCQ (Single Correct Answer)

JEE Main 2024 (Online) 9th April Evening Shift

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of $$2: 1$$. After disintegration they will move :

JEE Main 2024 (Online) 9th April Evening Shift

The energy released in the fusion of $$2 \mathrm{~kg}$$ of hydrogen deep in the sun is $$E_H$$ and the energy released in the fission of $$2 \mathrm{~...

JEE Main 2024 (Online) 9th April Evening Shift

A hydrogen atom in ground state is given an energy of $$10.2 \mathrm{~eV}$$. How many spectral lines will be emitted due to transition of electrons?...

JEE Main 2024 (Online) 9th April Morning Shift

The energy equivalent of $$1 \mathrm{~g}$$ of substance is :

JEE Main 2024 (Online) 1st February Evening Shift

From the statements given below :
(A) The angular momentum of an electron in $n^{\text {th }}$ orbit is an integral multiple of $\hbar$.
(B) Nuclear f...

JEE Main 2024 (Online) 1st February Morning Shift

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly :

JEE Main 2024 (Online) 31st January Evening Shift

The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is :

JEE Main 2024 (Online) 31st January Morning Shift

If the wavelength of the first member of Lyman series of hydrogen is $$\lambda$$. The wavelength of the second member will be

JEE Main 2024 (Online) 30th January Evening Shift

An electron revolving in $$n^{\text {th }}$$ Bohr orbit has magnetic moment $$\mu_n$$. If $$\mu_n \alpha \cdot n^x$$, the value of $$x$$ is

JEE Main 2024 (Online) 30th January Evening Shift

In a nuclear fission reaction of an isotope of mass $$M$$, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in te...

JEE Main 2024 (Online) 30th January Morning Shift

The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the 5th excited state of a hydrogen atom is :...

JEE Main 2024 (Online) 29th January Evening Shift

Given below are two statements:
Statement I : Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the elec...

JEE Main 2024 (Online) 29th January Morning Shift

The explosive in a Hydrogen bomb is a mixture of $${ }_1 \mathrm{H}^2,{ }_1 \mathrm{H}^3$$ and $${ }_3 \mathrm{Li}^6$$ in some condensed form. The cha...

JEE Main 2024 (Online) 27th January Evening Shift

The atomic mass of $${ }_6 \mathrm{C}^{12}$$ is $$12.000000 \mathrm{~u}$$ and that of $${ }_6 \mathrm{C}^{13}$$ is $$13.003354 \mathrm{~u}$$. The requ...

JEE Main 2024 (Online) 27th January Morning Shift

The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth stationary orbit will be:

JEE Main 2023 (Online) 15th April Morning Shift

The half-life of a radioactive nucleus is 5 years. The fraction of the original sample that would decay in 15 years is:

JEE Main 2023 (Online) 13th April Evening Shift

Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$
Assertion A : The bindi...

JEE Main 2023 (Online) 13th April Morning Shift

$$_{92}^{238}A \to _{90}^{234}B + _2^4D + Q$$
In the given nuclear reaction, the approximate amount of energy released will be:
[Given, mass of $${ }_...

JEE Main 2023 (Online) 12th April Morning Shift

A $$12.5 \mathrm{~eV}$$ electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:

JEE Main 2023 (Online) 11th April Evening Shift

The energy of $$\mathrm{He}^{+}$$ ion in its first excited state is, (The ground state energy for the Hydrogen atom is $$-13.6 ~\mathrm{eV})$$ :...

JEE Main 2023 (Online) 11th April Morning Shift

Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If $$\lambda_{A}$$ and $$\l...

JEE Main 2023 (Online) 10th April Evening Shift

The half life of a radioactive substance is T. The time taken, for disintegrating $$\frac{7}{8}$$th part of its original mass will be:

JEE Main 2023 (Online) 10th April Morning Shift

The angular momentum for the electron in Bohr's orbit is L. If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in...

JEE Main 2023 (Online) 8th April Evening Shift

A radio active material is reduced to $$1 / 8$$ of its original amount in 3 days. If $$8 \times 10^{-3} \mathrm{~kg}$$ of the material is left after 5...

JEE Main 2023 (Online) 8th April Evening Shift

The waves emitted when a metal target is bombarded with high energy electrons are

JEE Main 2023 (Online) 8th April Morning Shift

For a nucleus $${ }_{\mathrm{A}}^{\mathrm{A}} \mathrm{X}$$ having mass number $$\mathrm{A}$$ and atomic number $$\mathrm{Z}$$
A. The surface energy pe...

JEE Main 2023 (Online) 6th April Evening Shift

A small particle of mass $$m$$ moves in such a way that its potential energy $$U=\frac{1}{2} m ~\omega^{2} r^{2}$$ where $$\omega$$ is constant and $$...

JEE Main 2023 (Online) 6th April Morning Shift

The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is :
...

JEE Main 2023 (Online) 1st February Evening Shift

An electron of a hydrogen like atom, having $$Z=4$$, jumps from $$4^{\text {th }}$$ energy state to $$2^{\text {nd }}$$ energy state. The energy relea...

JEE Main 2023 (Online) 1st February Morning Shift

The mass of proton, neutron and helium nucleus are respectively $$1.0073~u,1.0087~u$$ and $$4.0015~u$$. The binding energy of helium nucleus is :...

JEE Main 2023 (Online) 31st January Evening Shift

The radius of electron's second stationary orbit in Bohr's atom is R. The radius of 3rd orbit will be

JEE Main 2023 (Online) 31st January Morning Shift

A free neutron decays into a proton but a free proton does not decay into neutron. This is because

JEE Main 2023 (Online) 30th January Evening Shift

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$
Assertion A: The nuclear d...

JEE Main 2023 (Online) 30th January Morning Shift

Speed of an electron in Bohr's $$7^{\text {th }}$$ orbit for Hydrogen atom is $$3.6 \times 10^{6} \mathrm{~m} / \mathrm{s}$$. The corresponding speed ...

JEE Main 2023 (Online) 29th January Evening Shift

Substance A has atomic mass number 16 and half life of 1 day. Another substance B has atomic mass number 32 and half life of $$\frac{1}{2}$$ day. If b...

JEE Main 2023 (Online) 29th January Morning Shift

If a radioactive element having half-life of $$30 \mathrm{~min}$$ is undergoing beta decay, the fraction of radioactive element remains undecayed afte...

JEE Main 2023 (Online) 25th January Evening Shift

The energy levels of an atom is shown in figure.
Which one of these transitions will result in the emission of a photon of wavelength 124.1 nm?
Given...

JEE Main 2023 (Online) 25th January Morning Shift

The ratio of the density of oxygen nucleus ($$_8^{16}O$$) and helium nucleus ($$_2^{4}\mathrm{He}$$) is

JEE Main 2023 (Online) 24th January Evening Shift

A photon is emitted in transition from n = 4 to n = 1 level in hydrogen atom. The corresponding wavelength for this transition is (given, h = 4 $$\tim...

JEE Main 2023 (Online) 24th January Morning Shift

Consider the following radioactive decay process
$$_{84}^{218}A\buildrel \alpha \over
\longrightarrow {A_1}\buildrel {{\beta ^ - }} \over
\longrigh...

JEE Main 2022 (Online) 29th July Evening Shift

Read the following statements :
(A) Volume of the nucleus is directly proportional to the mass number.
(B) Volume of the nucleus is independent of mas...

JEE Main 2022 (Online) 29th July Morning Shift

Find the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) second permitted energy level to the fir...

JEE Main 2022 (Online) 28th July Evening Shift

A radioactive sample decays $$\frac{7}{8}$$ times its original quantity in 15 minutes. The half-life of the sample is

JEE Main 2022 (Online) 28th July Morning Shift

The half life period of a radioactive substance is 60 days. The time taken for $$\frac{7}{8}$$th of its original mass to disintegrate will be :

JEE Main 2022 (Online) 27th July Evening Shift

The activity of a radioactive material is $$6.4 \times 10^{-4}$$ curie. Its half life is 5 days. The activity will become $$5 \times 10^{-6}$$ curie a...

JEE Main 2022 (Online) 27th July Morning Shift

What is the half-life period of a radioactive material if its activity drops to $$1 / 16^{\text {th }}$$ of its initial value in 30 years?

JEE Main 2022 (Online) 26th July Evening Shift

A nucleus of mass $$M$$ at rest splits into two parts having masses $$\frac{M^{\prime}}{3}$$ and $${{2M'} \over 3}(M' ...

JEE Main 2022 (Online) 26th July Evening Shift

Mass numbers of two nuclei are in the ratio of $$4: 3$$. Their nuclear densities will be in the ratio of

JEE Main 2022 (Online) 26th July Morning Shift

The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 dis...

JEE Main 2022 (Online) 25th July Evening Shift

Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength $$\lambda$$. The value of principal quantum number '$$n$...

JEE Main 2022 (Online) 25th July Morning Shift

The momentum of an electron revolving in $$\mathrm{n}^{\text {th }}$$ orbit is given by :
(Symbols have their usual meanings)

JEE Main 2022 (Online) 25th July Morning Shift

The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by :

JEE Main 2022 (Online) 30th June Morning Shift

A hydrogen atom in ground state absorbs 12.09 eV of energy. The orbital angular momentum of the electron is increased by :

JEE Main 2022 (Online) 29th June Evening Shift

In the following nuclear reaction,
$$D\buildrel \alpha \over
\longrightarrow {D_1}\buildrel {{\beta ^ - }} \over
\longrightarrow {D_2}\buildrel \al...

JEE Main 2022 (Online) 29th June Morning Shift

The activity of a radioactive material is 2.56 $$\times$$ 10$$-$$3 Ci. If the half life of the material is 5 days, after how many days the activity wi...

JEE Main 2022 (Online) 28th June Evening Shift

Following statements related to radioactivity are given below :
(A) Radioactivity is a random and spontaneous process and is dependent on physical and...

JEE Main 2022 (Online) 28th June Morning Shift

The Q-value of a nuclear reaction and kinetic energy of the projectile particle, Kp are related as :

JEE Main 2022 (Online) 27th June Evening Shift

Given below are two statements :
Statement I : In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit (E1...

JEE Main 2022 (Online) 27th June Morning Shift

A hydrogen atom in its ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of :
(...

JEE Main 2022 (Online) 26th June Evening Shift

A radioactive nucleus can decay by two different processes. Half-life for the first process is 3.0 hours while it is 4.5 hours for the second process....

JEE Main 2022 (Online) 26th June Morning Shift

How many alpha and beta particles are emitted when Uranium 92U238 decays to lead 82Pb206 ?

JEE Main 2022 (Online) 25th June Evening Shift

Which of the following figure represents the variation of $${l_n}\left( {{R \over {{R_0}}}} \right)$$ with $${l_n}A$$ (if R = radius of a nucleus and ...

JEE Main 2022 (Online) 25th June Morning Shift

The ratio for the speed of the electron in the 3rd orbit of He+ to the speed of the electron in the 3rd orbit of hydrogen atom will be :...

JEE Main 2022 (Online) 24th June Evening Shift

In Bohr's atomic model of hydrogen, let K, P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the ...

JEE Main 2022 (Online) 24th June Morning Shift

Choose the correct option from the following options given below :

JEE Main 2022 (Online) 24th June Morning Shift

Nucleus A is having mass number 220 and its binding energy per nucleon is 5.6 MeV. It splits in two fragments 'B' and 'C' of mass numbers 105 and 115....

JEE Main 2021 (Online) 1st September Evening Shift

The half life period of radioactive element x is same as the mean life time of another radioactive element y. Initially they have the same number of a...

JEE Main 2021 (Online) 31st August Morning Shift

A sample of a radioactive nucleus A disintegrates to another radioactive nucleus B, which in turn disintegrates to some other stable nucleus C. Plot o...

JEE Main 2021 (Online) 27th August Morning Shift

There are 1010 radioactive nuclei in a given radioactive element, its half-life time is 1 minute. How many nuclei will remain after 30 seconds? $$\lef...

JEE Main 2021 (Online) 26th August Evening Shift

At time t = 0, a material is composed of two radioactive atoms A and B, where NA(0) = 2NB(0). The decay constant of both kind of radioactive atoms is ...

JEE Main 2021 (Online) 26th August Morning Shift

A particular hydrogen like ion emits radiation of frequency 2.92 $$\times$$ 1015 Hz when it makes transition from n = 3 to n = 1. The frequency in Hz ...

JEE Main 2021 (Online) 27th July Evening Shift

Consider the following statements :A. Atoms of each element emit characteristics spectrum.B. According to Bohr's Postulate, an electron in a hydrogen ...

JEE Main 2021 (Online) 27th July Morning Shift

If 'f' denotes the ratio of the number of nuclei decayed (Nd) to the number of nuclei at t = 0 (N0) then for a collection of radioactive nuclei, the r...

JEE Main 2021 (Online) 25th July Morning Shift

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed a...

JEE Main 2021 (Online) 25th July Morning Shift

The half-life of $${}^{198}Au$$ is 3 days. If atomic weight of $${}^{198}Au$$ is 198 g/mol then the activity of 2 mg of $${}^{198}Au$$ is [in disinteg...

JEE Main 2021 (Online) 22th July Evening Shift

A nucleus with mass number 184 initially at rest emits an $$\alpha$$-particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy...

JEE Main 2021 (Online) 20th July Evening Shift

For a certain radioactive process the graph between In R and t(sec) is obtained as shown in the figure. Then the value of half life for the unknown ra...

JEE Main 2021 (Online) 20th July Morning Shift

A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years respectively. What will be the ti...

JEE Main 2021 (Online) 20th July Morning Shift

A nucleus of mass M emits $$\gamma$$ -ray photon of frequency 'v'. The loss of internal energy by the nucleus is :[Take 'c' as the speed of electromag...

JEE Main 2021 (Online) 18th March Evening Shift

The decay of a proton to neutron is :

JEE Main 2021 (Online) 18th March Morning Shift

Imagine that the electron in a hydrogen atom is replaced by a muon ($$\mu$$). The mass of muon particle is 207 times that of an electron and charge is...

JEE Main 2021 (Online) 18th March Morning Shift

A radioactive sample disintegrates via two independent decay processes having half lives $$T_{1/2}^{(1)}$$ and $$T_{1/2}^{(2)}$$ respectively. The eff...

JEE Main 2021 (Online) 17th March Evening Shift

The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra is lying in the visible region?

JEE Main 2021 (Online) 17th March Morning Shift

If an electron is moving in the nth orbit of the hydrogen atom, then its velocity (vn) for the nth orbit is given as :...

JEE Main 2021 (Online) 17th March Morning Shift

Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom?

JEE Main 2021 (Online) 16th March Evening Shift

Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.

JEE Main 2021 (Online) 16th March Evening Shift

The half-life of Au198 is 2.7 days. The activity of 1.50 mg of Au198 if its atomic weight is 198 g mol$$-$$1 is, (Na = 6 $$\times$$ 1023/mol)....

JEE Main 2021 (Online) 26th February Evening Shift

A radioactive sample is undergoing $$\alpha$$ decay. At any time t1, its activity is A and another time t2, the activity is $${A \over 5}$$. What is t...

JEE Main 2021 (Online) 26th February Morning Shift

If $$\lambda$$1 and $$\lambda$$2 are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value ...

JEE Main 2021 (Online) 25th February Evening Shift

The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from n = 2 to n = 1 state is :

JEE Main 2021 (Online) 25th February Morning Shift

Two radioactive substances X and Y originally have N1 and N2 nuclei respectively. Half life of X is half of the half life of Y. After three half lives...

JEE Main 2021 (Online) 24th February Evening Shift

According to Bohr atomic model, in which of the following transitions will the frequency be maximum?

JEE Main 2021 (Online) 24th February Morning Shift

In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked A, B, C, D and E.The transitions A, B and C...

JEE Main 2020 (Online) 6th September Evening Slot

Given the masses of various atomic particles
mp = 1.0072 u, mn = 1.0087 u, me = 0.000548 u,
$${m_{\overline v }}$$ = 0, md = 2.0141 u, where p $$ \equ...

JEE Main 2020 (Online) 6th September Morning Slot

You are given that Mass of $${}_3^7Li$$ = 7.0160u,
Mass of $${}_2^4He$$ = 4.0026u
and Mass of $${}_1^1H$$ = 1.0079u.
When 20 g of $${}_3^7Li$$ is conv...

JEE Main 2020 (Online) 5th September Evening Slot

A radioactive nucleus decays by two different
processes. The half life for the first process is
10 s and that for the second is 100 s. The
effective h...

JEE Main 2020 (Online) 5th September Morning Slot

Activities of three radioactive substances A, B
and C are represented by the curves A, B and
C, in the figure. Then their half-lives
$${T_{{1 \over 2}...

JEE Main 2020 (Online) 4th September Evening Slot

Find the Binding energy per neucleon for $${}_{50}^{120}Sn$$. Mass of proton mp
= 1.00783 U, mass of neutron
mn
= 1.00867 U and mass of tin nucleus ...

JEE Main 2020 (Online) 3rd September Evening Slot

The radius R of a nucleus of mass number A can be estimated by the formula R = (1.3 $$ \times $$ 10–15)A1/3 m.
It follows that the mass density of a n...

JEE Main 2020 (Online) 3rd September Evening Slot

Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential
difference. The ratio of final speeds of hydrogen a...

JEE Main 2020 (Online) 3rd September Morning Slot

In a radioactive material, fraction of active
material remaining after time t is 9/16. The
fraction that was remaining after t/2 is

JEE Main 2020 (Online) 2nd September Evening Slot

In a hydrogen atom the electron makes a
transition from (n + 1)th level to the nth level.
If n >> 1, the frequency of radiation emitted is
propo...

JEE Main 2020 (Online) 2nd September Morning Slot

In a reactor, 2 kg of 92U235 fuel is fully used up
in 30 days. The energy released per fission is
200 MeV. Given that the Avogadro number,
N = 6.023 $...

JEE Main 2020 (Online) 9th January Evening Slot

The energy required to ionise a hydrogen like
ion in its ground state is 9 Rydbergs. What is
the wavelength of the radiation emitted when
the electron...

JEE Main 2020 (Online) 8th January Morning Slot

The graph which depicts the results of
Rutherford gold foil experiment with
$$\alpha $$-particales is :
$$\theta $$ : Scattering angle
Y : Number of s...

JEE Main 2020 (Online) 7th January Evening Slot

The activity of a radioactive sample falls from 700 s–1 to 500 s–1 in 30 minutes. Its half life is close
to:

JEE Main 2020 (Online) 7th January Morning Slot

The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6 $$ \times $$ 10-16 s. The frequency of revolution of the...

JEE Main 2019 (Online) 12th April Evening Slot

Consider an electron in a hydrogen atom revolving in its second excited state (having radius 4.65 $$\mathop A\limits^o $$). The
de-Broglie wavelength ...

JEE Main 2019 (Online) 12th April Evening Slot

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and
subsequently to the first excited state. The ...

JEE Main 2019 (Online) 12th April Evening Slot

Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively, If initially a sample
has equal number of nuclei, then after...

JEE Main 2019 (Online) 12th April Morning Slot

An excited He+
ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm, in making a
transition to ground state. The quantum number...

JEE Main 2019 (Online) 10th April Evening Slot

Two radioactive substances A and B have decay constants 5$$\lambda $$ and $$\lambda $$ respectively. At t = 0, a sample has the
same number of the two...

JEE Main 2019 (Online) 10th April Evening Slot

In Li+ +, electron in first Bohr orbit is excited to a level by a radiation of wavelength $$\lambda $$. When the ion gets
deexcited to the ground stat...

JEE Main 2019 (Online) 10th April Morning Slot

Two radioactive materials A and B have decay
constants 10$$\lambda $$ and $$\lambda $$, respectively. It initially
they have the same number of nuclei...

JEE Main 2019 (Online) 9th April Evening Slot

A He+ ion is in its first excited state. Its
ionization energy is :-

JEE Main 2019 (Online) 9th April Morning Slot

Taking the wavelength of first Balmer line in
hydrogen spectrum (n = 3 to n = 2) as 660 nm,
the wavelength of the 2nd Balmer line (n = 4 to
n = 2) wil...

JEE Main 2019 (Online) 8th April Evening Slot

The ratio of mass densities of nuclei of 40Ca
and 16O is close to :-

JEE Main 2019 (Online) 8th April Morning Slot

Radiation coming from transitions
n = 2 to n = 1 of hydrogen atoms fall on He+
ions in n = 1 and n = 2 states. The possible
transition of helium ions ...

JEE Main 2019 (Online) 12th January Evening Slot

In a radioactive decay chain, the initial nucleus is $${}_{90}^{232}$$Th. At the end there are 6 $$\alpha $$-particles and 4 $$\beta $$-particles whic...

JEE Main 2019 (Online) 12th January Morning Slot

A particle of mass m moves in a circular orbit in a central potential field U(r) = $${1 \over 2}$$ kr2. If Bohr 's
quantization conditions are applied...

JEE Main 2019 (Online) 11th January Evening Slot

In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is $$\lambda $$. If an electron j...

JEE Main 2019 (Online) 11th January Morning Slot

A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980$$\mathop A\limits^ \circ $$. The radius of the atom...

JEE Main 2019 (Online) 10th January Evening Slot

Consider the nuclear fission
Ne20 $$ \to $$ 2He4 + C12
Given that the binding energy/ nucleon of Ne20, He4 and C12 are, respectively, 8.03 MeV, ...

JEE Main 2019 (Online) 10th January Morning Slot

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 se...

JEE Main 2019 (Online) 9th January Evening Slot

At a given instant, say t = 0, two radioactive substance A and B have equal activities. the ratio $${{{R_B}} \over {{R_A}}}$$ of their activities aft...

JEE Main 2019 (Online) 9th January Morning Slot

A sample of radioactive material A, that has an activity of 10 mCi(1 Ci = 3.7 $$ \times $$ 1010 decays/s), has twice the number of nuclei as another s...

JEE Main 2018 (Online) 16th April Morning Slot

At some instant, a radioactive sample S1 having an activity 5 $$\mu $$Ci has twice the number of nuclei as another sample S2 which has an activity of...

JEE Main 2018 (Offline)

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let
$${\lambda _n}$$, $${\lambda _g}$$ be the de ...

JEE Main 2018 (Offline)

If the series limit frequency of the Lyman series is $${\nu _L}$$, then the series limit frequency of the Pfund series is:

JEE Main 2018 (Offline)

It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its
energy is pd; while for its simila...

JEE Main 2018 (Online) 15th April Evening Slot

An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8 : 27. The ratio of the radii of the nuclei ...

JEE Main 2018 (Online) 15th April Evening Slot

Muon ($$\mu $$$$-$$) is a negatively charged (|q| = |e|) particle with a mass m$$\mu $$ = 200 me, where me is the mass of the electron and e is the el...

JEE Main 2018 (Online) 15th April Morning Slot

The energy required to remove the electron from a singly ionized Helium atom is $$2.2$$ times the energies required to remove an electron from Helium ...

JEE Main 2018 (Online) 15th April Morning Slot

A solution containing active cobalt $${^{60}_{27}}Co$$ having activity of $$0.8$$ $$\mu Ci$$ and decay constant $$\lambda $$ is injected in an animal'...

JEE Main 2017 (Online) 9th April Morning Slot

The acceleration of an electron in the first orbit of the hydrogen atom (n = 1) is :

JEE Main 2017 (Online) 9th April Morning Slot

Imagine that a reactor converts all given mass into energy and that it operates at a power level of 109 watt. The mass of the fuel consumed per hour ...

JEE Main 2017 (Online) 8th April Morning Slot

According to Bohr’s theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the nth...

JEE Main 2017 (Online) 8th April Morning Slot

Two deuterons undergo nuclear fusion to form a Helium nucleus. Energy released in this process is : (given binding energy per nucleon for deuteron = 1...

JEE Main 2017 (Offline)

Some energy levels of a molecule are shown in the figure. The
ratio of the wavelengths r = $${{\lambda _1}}$$/$${{\lambda _2}}$$, is given by:
...

JEE Main 2017 (Offline)

A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At
sometime t, the ratio of the number of B to t...

JEE Main 2016 (Online) 9th April Morning Slot

A hydrogen atom makes a transition from n = 2 to n = 1 and emits a photon. This photon strikes a doubly ionized lithium atom (z = 3) in excited state ...

JEE Main 2016 (Offline)

Half-lives of two radioactive elements $$A$$ and $$B$$ are $$20$$ minutes and $$40$$ minutes, respectively. Initially, the samples have equal number o...

JEE Main 2015 (Offline)

As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion :

JEE Main 2014 (Offline)

Hydrogen $$\left( {{}_1{H^1}} \right)$$, Deuterium $$\left( {{}_1{H^2}} \right)$$, singly ionised Helium $${\left( {{}_2H{e^4}} \right)^ + }$$ and dou...

JEE Main 2014 (Offline)

The radiation corresponding to $$3 \to 2$$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to...

JEE Main 2013 (Offline)

In a hydrogen like atom electron make transition from an energy level with quantum number $$n$$ to another with quantum number $$\left( {n - 1} \right...

AIEEE 2012

Hydrogen atom is excited from ground state to another state with principal quantum number equal to $$4.$$ Then the number of spectral lines in the emi...

AIEEE 2012

Assume that a neutron breaks into a proton and an electron. The energy released during this process is : (mass of neutron $$ = 1.6725 \times {10^{ - ...

AIEEE 2012

A diatomic molecule is made of two masses $${m_1}$$ and $${m_2}$$ which are separated by a distance $$r.$$ If we calculate its rotational energy by ap...

AIEEE 2011

Energy required for the electron excitation in $$L{i^{ + + }}$$ from the first to the third Bohr orbit is :

AIEEE 2011

The half life of a radioactive substance is $$20$$ minutes. The approximate time interval $$\left( {{t_2} - {t_1}} \right)$$ between the time $${{t_2}...

AIEEE 2010

A nucleus of mass $$M+$$$$\Delta m$$ is at rest and decays into two daughter nuclei of equal mass $${M \over 2}$$ each. Speed of light is $$c.$$
The ...

AIEEE 2010

A nucleus of mass $$M+$$$$\Delta m$$ is at rest and decays into two daughter nuclei of equal mass $${M \over 2}$$ each. Speed of light is $$c.$$
The ...

AIEEE 2010

A radioactive nucleus (initial mass number $$A$$ and atomic number $$Z$$ emits $$3\,\alpha $$- particles and $$2$$ positrons. The ratio of number of n...

AIEEE 2009

The transition from the state $$n=4$$ to $$n=3$$ in a hydrogen like atom result in ultra violet radiation. Infrared radiation will be obtained in the...

AIEEE 2009

The above is a plot of binding energy per nucleon $${E_b},$$ against the nuclear mass $$M;A,B,C,D,E,F$$ correspond to different nuclei. Consider fou...

AIEEE 2008

This question contains Statement- 1 and Statement- 2. Of the four choices given after the statements, choose the one that best describes the two sta...

AIEEE 2008

Suppose an electron is attracted towards the origin by a force $${k \over r}$$ where $$'k'$$ is a constant and $$'r'$$ is the distance of the electron...

AIEEE 2007

If $${M_O}$$ is the mass of an oxygen isotope $${}_8{O^{17}}$$ , $${M_p}$$ and $${M_N}$$ are the masses of a proton and neutron respectively, the nucl...

AIEEE 2007

In gamma ray emission from a nucleus

AIEEE 2007

The half-life period of a ratio-active element $$X$$ is same as the mean life time of another ratio-active element $$Y.$$ Initially they have the same...

AIEEE 2007

Which of the following transitions in hydrogen atoms emit photons of highest frequency ?

AIEEE 2006

An alpha nucleus of energy $${1 \over 2}m{v^2}$$ bombards a heavy nuclear target of charge $$Ze$$. Then the distance of closest approach for the alpha...

AIEEE 2006

When $${}_3L{i^7}$$ nuclei are bombarded by protons, and the resultant nuclei are $${}_4B{e^8}$$, the emitted particles will be

AIEEE 2006

If the binding energy per nucleon in $${}_3^7Li$$ and $${}_2^4He$$ nuclei are $$5.60$$ $$MeV$$ and $$7.06$$ $$MeV$$ respectively, then in the reaction...

AIEEE 2006

The $$'rad'$$ is the correct unit used to report the measurement of

AIEEE 2006

The energy spectrum of $$\beta $$-particles [ number $$N(E)$$ as a function of $$\beta $$-energy $$E$$ ] emitted from a radioactive source is

AIEEE 2005

If radius of the $$\matrix{
{27} \cr
{13} \cr
} $$ $$Al$$ nucleus is estimated to be $$3.6$$ fermi then the radius of $$\matrix{
{125} ...

AIEEE 2005

Starting with a sample of pure $${}^{66}Cu,{7 \over 8}$$ of it decays into $$Zn$$ in $$15$$ minutes. The corresponding half life is

AIEEE 2005

The intensity of gamma radiation from a given source is $$L$$. On passing through $$36$$ $$mm$$ of lead, it is reduced to $${{\rm I} \over 8}.$$ The t...

AIEEE 2005

A nuclear transformation is denoted by $$X\left( {n,\alpha } \right)\matrix{
7 \cr
3 \cr
} Li.$$ Which of the following is the nucleus of ...

AIEEE 2005

The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy...

AIEEE 2004

An $$\alpha $$-particle of energy $$5$$ $$MeV$$ is scattered through $${180^ \circ }$$ by a fixed uranium nucleus. The distance of closest approach is...

AIEEE 2004

The binding energy per nucleon of deuteron $$\left( {{}_1^2\,H} \right)$$ and helium nucleus $$\left( {{}_2^4\,He} \right)$$ is $$1.1$$ $$MeV$$ and $$...

AIEEE 2004

A nucleus disintegrated into two nuclear parts which have their velocities in the ratio of $$2:1.$$ The ratio of their nuclear sizes will be

AIEEE 2003

Which of the following radiations has the least wavelength ?

AIEEE 2003

When a $${U^{238}}$$ nucleus originally at rest, decays by emitting an alpha particle having a speed $$'u',$$ the recoil speed of the residual nucleus...

AIEEE 2003

A radioactive sample at any instant has its disintegration rate $$5000$$ disintegrations per minute. After $$5$$ minutes, the rate is $$1250$$ disinte...

AIEEE 2003

A nucleus with $$Z=92$$ emits the following in a sequence:
$$$\alpha ,{\beta ^ - },{\beta ^ - },\alpha ,\alpha ,\alpha ,\alpha ,\alpha ,{\beta ^ - },...

AIEEE 2003

Which of the following atoms has the lowest ionization potential ?

AIEEE 2003

The wavelengths involved in the spectrum of deuterium $$\left( {{}_1^2\,D} \right)$$ are slightly different from that of hydrogen spectrum, because

AIEEE 2003

In the nuclear fusion reaction
$$${}_1^2H + {}_1^3H \to {}_2^4He + n$$$
given that the repulsive potential energy between the two nuclei is $$ \sim 7...

AIEEE 2003

Which of the following cannot be emitted by radioactive substances during their decay ?

AIEEE 2003

If the binding energy of the electron in a hydrogen atom is $$13.6eV,$$ the energy required to remove the electron from the first excited state of $$L...

AIEEE 2002

If $$13.6$$ $$eV$$ energy is required to ionize the hydrogen atom, then the energy required to remove an electron from $$n=2$$ is

AIEEE 2002

At a specific instant emission of radioactive compound is deflected in a magnetic field. The compound can emit
$$\eqalign{
& \left( i \right)\,...

AIEEE 2002

If $${N_0}$$ is the original mass of the substance of half-life period $${t_{1/2}} = 5$$ years, then the amount of substance left after $$15$$ years i...

## Numerical

JEE Main 2024 (Online) 9th April Morning Shift

A star has $$100 \%$$ helium composition. It starts to convert three $${ }^4 \mathrm{He}$$ into one $${ }^{12} \mathrm{C}$$ via triple alpha process a...

JEE Main 2024 (Online) 1st February Evening Shift

A particular hydrogen-like ion emits the radiation of frequency $3 \times 10^{15} \mathrm{~Hz}$ when it makes transition from $n=2$ to $n=1$. The freq...

JEE Main 2024 (Online) 1st February Morning Shift

The radius of a nucleus of mass number 64 is 4.8 fermi. Then the mass number of another nucleus having radius of 4 fermi is $\frac{1000}{x}$, where $x...

JEE Main 2024 (Online) 31st January Evening Shift

A nucleus has mass number $$A_1$$ and volume $$V_1$$. Another nucleus has mass number $$A_2$$ and Volume $$V_2$$. If relation between mass number is $...

JEE Main 2024 (Online) 31st January Morning Shift

The mass defect in a particular reaction is $$0.4 \mathrm{~g}$$. The amount of energy liberated is $$n \times 10^7 \mathrm{~kWh}$$, where $$n=$$ _____...

JEE Main 2024 (Online) 30th January Morning Shift

A electron of hydrogen atom on an excited state is having energy $$\mathrm{E}_{\mathrm{n}}=-0.85 \mathrm{~eV}$$. The maximum number of allowed transit...

JEE Main 2024 (Online) 29th January Evening Shift

Hydrogen atom is bombarded with electrons accelerated through a potential difference of $$\mathrm{V}$$, which causes excitation of hydrogen atoms. If ...

JEE Main 2024 (Online) 29th January Morning Shift

When a hydrogen atom going from $$n=2$$ to $$n=1$$ emits a photon, its recoil speed is $$\frac{x}{5} \mathrm{~m} / \mathrm{s}$$. Where $$x=$$ ________...

JEE Main 2024 (Online) 27th January Evening Shift

If Rydberg's constant is $$R$$, the longest wavelength of radiation in Paschen series will be $$\frac{\alpha}{7 R}$$, where $$\alpha=$$ ________....

JEE Main 2024 (Online) 27th January Morning Shift

In a nuclear fission process, a high mass nuclide $$(A \approx 236)$$ with binding energy $$7.6 \mathrm{~MeV} /$$ Nucleon dissociated into middle mass...

JEE Main 2023 (Online) 15th April Morning Shift

As per given figure $A, B$ and $C$ are the first, second and third excited energy levels of hydrogen atom respectively. If the ratio of the two wavele...

JEE Main 2023 (Online) 13th April Morning Shift

The radius of $$2^{\text {nd }}$$ orbit of $$\mathrm{He}^{+}$$ of Bohr's model is $$r_{1}$$ and that of fourth orbit of $$\mathrm{Be}^{3+}$$ is repres...

JEE Main 2023 (Online) 12th April Morning Shift

A common example of alpha decay is $${ }_{92}^{238} \mathrm{U} \longrightarrow{ }_{90}^{234} \mathrm{Th}+{ }_{2} \mathrm{He}^{4}+\mathrm{Q}$$
Given :
...

JEE Main 2023 (Online) 11th April Evening Shift

A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is $$1: 2^{1 / 3}$$. Their respective speed have a rat...

JEE Main 2023 (Online) 10th April Evening Shift

If 917 $$\mathop A\limits^o $$ be the lowest wavelength of Lyman series then the lowest wavelength of Balmer series will be ___________ $$\mathop A\li...

JEE Main 2023 (Online) 10th April Morning Shift

The decay constant for a radioactive nuclide is 1.5 $$\times$$ 10$$^{-5}$$ s$$^{-1}$$. Atomic weight of the substance is 60 g mole$$^{-1}$$, ($$N_A=6\...

JEE Main 2023 (Online) 8th April Evening Shift

The ratio of wavelength of spectral lines $$\mathrm{H}_{\alpha}$$ and $$\mathrm{H}_{\beta}$$ in the Balmer series is $$\frac{x}{20}$$. The value of $$...

JEE Main 2023 (Online) 8th April Morning Shift

A nucleus with mass number 242 and binding energy per nucleon as $$7.6~ \mathrm{MeV}$$ breaks into two fragment each with mass number 121. If each fra...

JEE Main 2023 (Online) 6th April Evening Shift

Experimentally it is found that $$12.8 ~\mathrm{eV}$$ energy is required to separate a hydrogen atom into a proton and an electron. So the orbital rad...

JEE Main 2023 (Online) 6th April Morning Shift

The radius of fifth orbit of the $$\mathrm{Li}^{++}$$ is __________ $$\times 10^{-12} \mathrm{~m}$$.
Take: radius of hydrogen atom $$ = 0.51\,\mathop ...

JEE Main 2023 (Online) 1st February Evening Shift

Nucleus A having $$Z=17$$ and equal number of protons and neutrons has $$1.2 ~\mathrm{MeV}$$ binding energy per nucleon.
Another nucleus $$\mathrm{B}$...

JEE Main 2023 (Online) 1st February Morning Shift

A light of energy $$12.75 ~\mathrm{eV}$$ is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its ...

JEE Main 2023 (Online) 31st January Evening Shift

If the binding energy of ground state electron in a hydrogen atom is $13.6\, \mathrm{eV}$, then, the energy required to remove the electron from the s...

JEE Main 2023 (Online) 31st January Morning Shift

For hydrogen atom, $$\lambda_{1}$$ and $$\lambda_{2}$$ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. T...

JEE Main 2023 (Online) 30th January Evening Shift

A radioactive nucleus decays by two different process. The half life of the first process is 5 minutes and that of the second process is $30 \mathrm{~...

JEE Main 2023 (Online) 29th January Morning Shift

A radioactive element $$_{92}^{242}$$X emits two $$\alpha$$-particles, one electron and two positrons. The product nucleus is represented by $$_{\math...

JEE Main 2023 (Online) 25th January Evening Shift

A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3 : 2. The ratio of their nuclear sizes will be $${\left( {{x...

JEE Main 2023 (Online) 25th January Morning Shift

The wavelength of the radiation emitted is $$\lambda_0$$ when an electron jumps from the second excited state to the first excited state of hydrogen a...

JEE Main 2023 (Online) 24th January Evening Shift

The energy released per fission of nucleus of $$^{240}$$X is 200 MeV. The energy released if all the atoms in 120g of pure $$^{240}$$X undergo fission...

JEE Main 2023 (Online) 24th January Morning Shift

Assume that protons and neutrons have equal masses. Mass of a nucleon is $$1.6\times10^{-27}$$ kg and radius of nucleus is $$1.5\times10^{-15}~\mathrm...

JEE Main 2022 (Online) 29th July Evening Shift

Two radioactive materials A and B have decay constants $$25 \lambda$$ and $$16 \lambda$$ respectively. If initially they have the same number of nucle...

JEE Main 2022 (Online) 28th July Morning Shift

A freshly prepared radioactive source of half life 2 hours 30 minutes emits radiation which is 64 times the permissible safe level. The minimum time, ...

JEE Main 2022 (Online) 26th July Evening Shift

Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below :
$${ }_{1}^{2} X+{ }_{1}^{2} X={ }_{2}^{4} Y$$
The bin...

JEE Main 2022 (Online) 26th July Morning Shift

In the hydrogen spectrum, $$\lambda$$ be the wavelength of first transition line of Lyman series. The wavelength difference will be "a$$\lambda$$'' be...

JEE Main 2022 (Online) 25th July Evening Shift

$${x \over {x + 4}}$$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its
(i) third permitted ener...

JEE Main 2022 (Online) 30th June Morning Shift

A hydrogen atom in its first excited state absorbs a photon of energy x $$\times$$ 10$$-$$2 eV and excited to a higher energy state where the potentia...

JEE Main 2022 (Online) 29th June Evening Shift

The half life of a radioactive substance is 5 years. After x years a given sample of the radioactive substance gets reduced to 6.25% of its initial va...

JEE Main 2022 (Online) 29th June Morning Shift

$$\sqrt {{d_1}} $$ and $$\sqrt {{d_2}} $$ are the impact parameters corresponding to scattering angles 60$$^\circ$$ and 90$$^\circ$$ respectively, whe...

JEE Main 2022 (Online) 27th June Morning Shift

A beam of monochromatic light is used to excite the electron in Li+ + from the first orbit to the third orbit. The wavelength of monochromatic light i...

JEE Main 2022 (Online) 24th June Evening Shift

A sample contains 10$$-$$2 kg each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of their atomic weights is 1 : 2. The...

JEE Main 2021 (Online) 27th August Evening Shift

X different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are exited to states with principal quantum number n = 6 ?...

JEE Main 2021 (Online) 27th July Evening Shift

The K$$\alpha$$ X-ray of molybdenum has wavelength 0.071 nm. If the energy of a molybdenum atoms with a K electron knocked out is 27.5 keV, the energy...

JEE Main 2021 (Online) 27th July Morning Shift

In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius 0.5 $$\mathop A\limits^o $$. If the speed of electron is 2.2 ...

JEE Main 2021 (Online) 27th July Morning Shift

A radioactive sample has an average life of 30 ms and is decaying. A capacitor of capacitance 200 $$\mu$$F is first charged and later connected with r...

JEE Main 2021 (Online) 25th July Evening Shift

From the given data, the amount of energy required to break the nucleus of aluminium $$_{13}^{27}$$Al is __________ x $$\times$$ 10$$-$$3 J.Mass of ne...

JEE Main 2021 (Online) 25th July Evening Shift

The nuclear activity of a radioactive element becomes $${\left( {{1 \over 8}} \right)^{th}}$$ of its initial value in 30 years. The half-life of radio...

JEE Main 2021 (Online) 20th July Evening Shift

A radioactive substance decays to $${\left( {{1 \over {16}}} \right)^{th}}$$ of its initial activity in 80 days. The half life of the radioactive subs...

JEE Main 2021 (Online) 17th March Evening Shift

A particle of mass m moves in a circular orbit in a central potential field U(r) = U0r4. If Bohr's quantization conditions are applied, radii of possi...

JEE Main 2021 (Online) 16th March Morning Shift

The first three spectral lines of H-atom in the Balmer series are given $$\lambda$$1, $$\lambda$$2, $$\lambda$$3 considering the Bohr atomic model, th...

JEE Main 2020 (Online) 5th September Morning Slot

A particle of mass 200 MeV/c2 collides with a
hydrogen atom at rest. Soon after the collision
the particle comes to rest, and the atom
recoils and goe...

JEE Main 2020 (Online) 8th January Evening Slot

The first member of the Balmer series of
hydrogen atom has a wavelength of 6561 Å.
The wavelength of the second member of the
Balmer series (in nm) is...