Atoms
61 JEE Physics previous year questions on Atoms — options free on every question; 6 include the answer & explanation free, the rest unlock with PYQ Pass.
Considering Bohr's atomic model for hydrogen atom :
(A) the energy of H atom in ground state is same as energy of \({\mathrm{He}}^{+}\)ion in its first excited state.
(B) the energy of H atom in ground state is same as that for \({\mathrm{Li}}^{++}\)ion in its second excited state.
(C) the energy of H atom in its ground state is same as that of \({\mathrm{He}}^{+}\)ion for its ground state.
(D) the energy of \({\mathrm{He}}^{+}\)ion in its first excited state is same as that for \({\mathrm{Li}}^{++}\)ion in its ground state
[JEE Main 2025, 2 Apr (Shift 1)]
(A), (B) only
According to Bohr’s atomic model, the energy of an electron in a hydrogen-like atom is:
\(E=−13.6\frac{{Z}^{2}}{{n}^{2}}\mathrm{eV}\)
Energy of H atom in ground state:
\(E=−13.6\mathrm{eV}\)
Energy of He⁺ ion in first excited state:
\(E=−13.6\frac{{2}^{2}}{{2}^{2}}\mathrm{eV}\)\(=−13.6\mathrm{eV}\)
Energy of Li²⁺ ion in second excited state:
\(E=−13.6\frac{{3}^{2}}{{3}^{2}}\mathrm{eV}\)\(=−13.6\mathrm{eV}\)
Final Answer:
\(\mathrm{Correct}\mathrm{options}=A,B\)
The number of spectral lines emitted by atomic hydrogen that is in the \({4}^{\text{th }}\) energy level, is:
[JEE Main 2025, 29 Jan (Shift 2)]
6
No. of spectral line \(=\frac{n(n-1)}{2}=\frac{4\times 3}{2}=6\)
Considering the Bohr model of hydrogen like atoms, the ratio of the ratio of the radius \({5}^{\text{th }}\) orbit of the electron in \({\mathrm{Li}}^{2+}\) and \({\mathrm{He}}^{+}\)is;
\(\frac{2}{3}\)
In Bohr's model, radius of \( n^\text{th} \) orbit in hydrogen-like atoms is given by:
\[r_n \propto \frac{n^2}{Z}\]
So for 5th orbit:
\[r_5 \propto \frac{25}{Z}\]
Now,
For Li\(^{2+}\), \( Z = 3 \Rightarrow r \propto \frac{25}{3} \)
For He\(^{+}\), \( Z = 2 \Rightarrow r \propto \frac{25}{2} \)
Taking ratio:
\[\frac{r_{Li^{2+}}}{r_{He^+}} = \frac{25/3}{25/2} = \frac{2}{3}\]
Bohr's model is applicable for single electron atom of atomic number \(Z\). Dependency of frequency of rotation of electron in \(n^{\text {th }}\) principal quantum number is proportional to
\(Z^2 / n^3\)
-
In Bohr’s atomic model, an electron revolves in a circular orbit with quantized angular momentum.
-
The frequency of revolution (\(f\)) is given by:
\(f=\frac{v}{2\pi r}\)where:
- \(v\) is the electron's speed in orbit,
- \(r\) is the radius of the orbit.
-
Velocity of electron in the \(n\)n-th orbit:
\({v}_{n}\propto \frac{Z}{n}\) -
Radius of the orbit:
\({r}_{n}\propto \frac{{n}^{2}}{Z}\)
Using \(f=\frac{v}{2\pi r}\)
\({f}_{n}\propto \frac{\frac{Z}{n}}{\frac{{n}^{2}}{Z}}\)
\({f}_{n}\propto \frac{{Z}^{2}}{{n}^{3}}\)
Angular momentum of an electron in a hydrogen atom is \(\frac{3h}{\pi }\), then the energy of the electron is ___________ eV.
[JEE Main 2026, 2 Apr (Shift 1)]
-0.38
Bohr quantization: \(L=nℏ=n\frac{h}{2\pi }\) Given: \(L=\frac{3h}{\pi }=6\frac{h}{2\pi }\)
\(\Rightarrow n=6\)
Energy of hydrogen atom:
\({E}_{n}=\frac{-13.6}{{n}^{2}}\)
\(E=\frac{-13.6}{36}\approx -0.38eV\)
Considering Bohr's atomic model for hydrogen atom :
(A) the energy of H atom in ground state is same as energy of \({\mathrm{He}}^{+}\)ion in its first excited state.
(B) the energy of H atom in ground state is same as that for \({\mathrm{Li}}^{++}\)ion in its second excited state.
(C) the energy of H atom in its ground state is same as that of \({\mathrm{He}}^{+}\)ion for its ground state.
(D) the energy of \({\mathrm{He}}^{+}\)ion in its first excited state is same as that for \({\mathrm{Li}}^{++}\)ion in its ground state
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If radius of first Bohr's orbit of H-atom is a. Then find the radius of 2nd Bohr's orbit of H-atom.
(Shift - I Memory Based)
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Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of \({\mathrm{Li}}^{++}\)ion in its ground state is given by \(\frac{1}{X}{a}_{0}\), where \(X=________.\) (Where \({\mathrm{a}}_{0}\) is the first Bohr's radius.):
[JEE Main 2025, 2 Apr (Shift 2)]
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In Rutherford's alpha-particle scattering experiment, only a few alpha particles rebound back because
A. The size of gold nucleus is very small as compared to the size of gold atom.
B. Alpha particle and gold nucleus have equal charge.
C. The impact parameter is minimum for a few alpha particles.
D. A few alpha particles have very high kinetic energy.
E. Only a few alpha particles undergo head-on collision with the nuclei.
Choose the correct answer from the options given below:
[04 April, 2026 (Shift-2)]
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Given below are two statements :
Statement (I) : The dimensions of Planck’s constant and angular momentum are same.
Statement (II) : In Bohr’s model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck’s constant.
In the light of the above statements, choose the most appropriate answer from the options given below :
[JEE Main 2025, 4 Apr (Shift 2)]
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Infrared light of wavelength \(900\text{ }\text{nm}\) is used for muscle pain relief. Which of the following transitions in the hydrogen atom can produce this wavelength?
(shift 1 Memory based)
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Considering the Bohr model of hydrogen like atoms, the ratio of the radius of \({5}^{\text{th }}\) orbit of the electron in \({\mathrm{Li}}^{2+}\) and \({\mathrm{He}}^{+}\)is:
[JEE Main 2025, 4 Apr (Shift 1)]
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In the hydrogen atom, the electron makes a transition from the higher orbit (i) to a lower orbit (f). The ratio of the radius of the orbits in given by \({r}_{i}:{r}_{f}=16:4\).
The wavelength of photon emitted due to this transition is_____ nm .
(Given Rydberg constant \(=1.0973\times {10}^{7}{\mathrm{m}}^{-1}\) )
[JEE Main 2026, 5 Apr (Shift 1)]
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The longest wavelength associated with Paschen series is : (Given \(R _{ H }=1.097 \times 10^7 SI\) unit)
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Statement 1: Graph of frequency f of X ray and atomic number Z of heavy nucleus is not straight line, in X ray emission.
Statement 2: Graph of square root of frequency \(\sqrt{\mathrm{f}}\) of X ray and atomic number Z of heavy nucleus is straight line, in X ray emission.
(Shift - II Memory Based)
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The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is :
[JEE Main 2021, 25 July (Shift 2)]
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The ratio of momentum of the photons of the \({1}^{\text{st }}\) and \({2}^{\text{nd }}\) line of Balmer series of Hydrogen atoms is \(\alpha /\beta\). The possible values of \(\alpha\) and \(\beta\) are:
[JEE Main 2026, 6 Apr (Shift 1)]
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An electron is moving in a magnetic field \(B\) in a circular orbit. Assume Bohr's quantization to be valid. Find the radius of the orbit in the 1st excited state.
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A hydrogen atom in ground state is given an energy of \(10.2 \ eV\). How many spectral lines will be emitted due to transition of electrons?
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If radius of first Bohr's orbit of H-atom is a. Then find the radius of 2nd Bohr's orbit of H-atom.
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A hydrogen atom in ground state is given an energy of \(10.2 \ eV\). How many spectral lines will be emitted due to transition of electrons?
[JEE Main 2024, 9 Apr (Shift 2)]
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If the wavelength of the first member of Lyman series of hydrogen is \( \lambda \). The wavelength of the second member will be:
[JEE Main 2023, 15 Apr (Shift 1)]
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The powers of two light sources \(S_1\) and \(S_2\) are in the ratio 2: 1. Source \(S_1\) emits \(2 \times 10^{15}\) photons per second at a wavelength of 600 nm . Find the number of photons per second emitted at a wavelength of 300 nm by \(S_2\).
(Shift - II Memory based)
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A hydrogen atom in ground state is given an energy of \(10.2 \ eV\). How many spectral lines will be emitted due to transition of electrons?
[JEE Main 2024, 9 Apr (Shift 2)]
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Given below are two statements :
Statement (I) : The dimensions of Planck’s constant and angular momentum are same.
Statement (II) : In Bohr’s model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck’s constant.
In the light of the above statements, choose the most appropriate answer from the options given below :
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If the wavelength of the first member of Lyman series of hydrogen is \( \lambda \). The wavelength of the second member will be;
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In a hydrogen like ion, the energy difference between the \({2}^{\text{nd }}\) excitation energy state and ground is \(108.8eV\) . The atomic number of the ion is:
[JEE Main 2025, 7 Apr (Shift 1)]
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An electron in the ground state of the hydrogen atom has the orbital radius of \(5.3\times {10}^{-11}\mathrm{m}\) while that for the electron in third excited state is \(8.48\times {10}^{-10}\mathrm{m}\). The ratio of the de Broglie wavelengths of electron in the ground state to that in the excited state is
[JEE Main 2025, 22 Jan (Shift 1)]
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For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is:
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A particle with initial velocity \({v}_{0}\) and charge q has an initial de Broglie wavelength \({\lambda }_{0}\). If an electric field \(\overset{⃗}{E}={E}_{0}\hat{k}\) is present in space, find the de Broglie wavelength of the particle at time \(t\).
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In a hydrogen like ion, the energy difference between the \({2}^{\text{nd }}\) excitation energy state and ground is \(108.8eV\) . The atomic number of the ion is;
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Statement 1: Graph of frequency f of X ray and atomic number Z of heavy nucleus is not straight line, in X ray emission.
Statement 2: Graph of square root of frequency \(\sqrt{\mathrm{f}}\) of X ray and atomic number Z of heavy nucleus is straight line, in X ray emission.
(Shift - II Memory Based)
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An electron is moving in a magnetic field \(B\) in a circular orbit. Assume Bohr's quantization to be valid. Find the radius of the orbit in the 1st excited state.
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Infrared light of wavelength \(900\text{ }\text{nm}\) is used for muscle pain relief. Which of the following transitions in the hydrogen atom can produce this wavelength?
(shift 1 Memory based)
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The number of spectral lines emitted by atomic hydrogen that is in the \({4}^{\text{th }}\) energy level, is
[JEE Main 2025, 29 Jan (Shift 2)]
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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The Bohr model is applicable to hydrogen and hydrogen-like atoms only.
Reason R : The formulation of Bohr model does not include repulsive force between electrons.
In the light of the above statements, choose the correct answer from the options given below :
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The angular momentum of an electron in a hydrogen atom is proportional to : (Where r is the radius of orbit of electron)
[JEE Main 2024, 5 Apr (Shift 2)]
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An electron in the ground state of the hydrogen atom has the orbital radius of \(5.3\times {10}^{-11}\mathrm{m}\) while that for the electron in third excited state is \(8.48\times {10}^{-10}\mathrm{m}\). The ratio of the de Broglie wavelengths of electron in the ground state to that in the excited state is:
[JEE Main 2025, 22 Jan (Shift 1)]
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For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is:
[JEE Main 2025, 7 Apr (Shift 1)]
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An electron transitions from the principal quantum state \(A\) to \(C\) by releasing a photon of wavelength 2000A˚, and from state \(B\) to \(C\) by releasing a photon of wavelength 6000A˚. What is the wavelength of the photon released during the transition from \(A\) to \(B\)?
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The powers of two light sources \(S_1\) and \(S_2\) are in the ratio 2: 1. Source \(S_1\) emits \(2 \times 10^{15}\) photons per second at a wavelength of 600 nm . Find the number of photons per second emitted at a wavelength of 300 nm by \(S_2\).
(Shift - II Memory based)
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The radius of electron's second stationary orbit in Bohr's atom is \(R\). The radius of 3rd orbit will be:
[JEE Main 2023, 31 Jan (Shift 2)]
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A photon is emitted in transition from \(n=4\) to \(n=1\) level in hydrogen atom. The corresponding wavelength for this transition is (given, \(h =4 \times 10^{-15} eVs\) ):
[JEE Main 2023, 24 Jan (Shift 2)]
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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 \(r\) is the distance of the particle from origin. Assuming Bohr's quantization of momentum and circular orbit, the radius of \(n^{\text {th }}\) orbit will be proportional to:
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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 \(r\) is the distance of the particle from origin. Assuming Bohr's quantization of momentum and circular orbit, the radius of \(n^{\text {th }}\) orbit will be proportional to:
[JEE Main 2023, 6 Apr (Shift 2)]
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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 released in this process, will be:
(Given \(R c h=13.6 eV\) ) Where \(R=\) Rydberg constant, \(c=\) Speed of light in vacuum, \(h=\) Planck's constant.[JEE Main 2023, 1 Feb (Shift 2)]
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Given below are two statements:
Statement-I: In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit \(\left(E_1\right)\) to higher energy orbit \(\left(E_2\right)\), is given as \(h f=E_1-E_2\).
Statement-II: The jumping of electron from higher energy orbit \(\left(E_2\right)\) to lower energy orbit \(E_1\) is associated with frequency of radiation given as \(f=\left(E_2-E_1\right) / h\).This condition is Bohr's frequency condition.
In the light of the above statements, choose the correct answer from the options given below:
[JEE Main 2022, 27 June (Shift 2)]
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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 released in this process, will be:
(Given \(R c h=13.6 eV\) ) Where \(R=\) Rydberg constant, \(c=\) Speed of light in vacuum, \(h=\) Planck's constant
[JEE Main 2023, 1 Feb (Shift 2)]
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In hydrogen spectrum, the shortest wavelength in the Balmer series is \(\lambda\). The shortest wavelength in the Bracket series is :
[NEET 2023]
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Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to:
[JEE Main 2021, 31 Aug (Shift 2)]
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An X-ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be:
[JEE Main 2021, 24 Feb (Shift 2)]
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An electron and proton are separated by a large distance. The electron starts approaching the proton with energy \(3 eV\). The proton captures the electron and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength 4000 \(\overset{^\circ }{A}\). What is the maximum kinetic energy of the emitted photoelectron?
[JEE Main 2021, 27 Jul (Shift 2)]
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The waves emitted when a metal target is bombarded with high energy electrons are:
[JEE Main 2023, 8 Apr (Shift 2)]
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A \(12.5 eV\) electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:
[JEE Main 2023, 12 Apr (Shift 1)]
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The radius of electron’s second stationary orbit in Bohr’s atom is R. The radius of 3rd orbit will be
[JEE Main 2023, 31 Jan (Shift 2)]
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If an electron is moving in the \(n^{\text {th }}\) orbit of the hydrogen atom, then its velocity \(\left( v _{ n }\right)\) for the \(n^{\text {th }}\) orbit is given as:
[JEE Main 2021, 17 Mar (Shift 1)]
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A free electron of \(2.6\ eV\) energy collides with a \(H^{+}\) ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon. \(\left( h = 6.6 \times 10^{- 34}\text{Js} \right)\)
[JEE Main 2021, 26 Aug (Shift 2)]
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A photon is emitted in transition from \(n=4\) to \(n=1\) level in hydrogen atom. The corresponding wavelength for this transition is (given, \(h=4 \times 10^{-15} \mathrm{eVs}\) ):
[JEE Main 2023, 24 Jan (Shift 2)]
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The waves emitted when a metal target is bombarded with high energy electrons are
[JEE Main 2023, 8 Apr (Shift 2)]
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The radius of electron's second stationary orbit in Bohr's atom is \(R\). The radius of 3rd orbit will be
[JEE Main 2023, 31 Jan (Shift 2)]
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