Atoms

An electron makes a transition from orbit n = 2 to orbit n = 1, in Bohr’s model of hydrogen atom. Consider change in magnitudes of its kinetic energy (K) and potential energy (U).

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:

A proton and an alpha particle having equal velocities approach a target nucleus. They come momentarily to rest and then reverse their directions. The ratio of the distance of closest approach of the proton to that of the alpha particle will be :

Which of the following statements is correct for alpha particle scattering experiment?

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)

The energy of an electron in the ground state of hydrogen atom is -13.6 eV . The kinetic and potential energy of the electron in the first excited state will be

An electron makes a transition from \(n=2\) level to \(n=1\) level in the Bohr model of a hydrogen atom. Its period of revolution :

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;

A proton and an alpha particle having equal velocities approach a target nucleus. They come momentarily to rest and then reverse their directions. The ratio of the distance of closest approach of the proton to that of the alpha particle will be :

A proton and an alpha particle having equal velocities approach a target nucleus. They come momentarily to rest and then reverse their directions. The ratio of the distance of closest approach of the proton to that of the alpha particle will be :

Which of the following statements is correct for alpha particle scattering experiment?

An alpha particle approaches a gold nucleus in Geiger-Marsden experiment with kinetic energy K. It momentarily stops at a distance \(d\) from the nucleus and reverses its direction. Then d is proportional to :

Energy levels A, B and C of an atom correspond to increasing values of energy i.e. \({\mathrm{E}}_{\mathrm{A}}<{\mathrm{E}}_{\mathrm{B}}<{\mathrm{E}}_{\mathrm{C}}\). Let \({\lambda }_{1},{\lambda }_{2}\) and \({\lambda }_{3}\) be the wavelengths of radiation corresponding to the transitions C to \(\mathrm{B}, \mathrm{B}\) to A and C to A , respectively. The correct relation between \({\lambda }_{1},{\lambda }_{2}\) and \({\lambda }_{3}\) is :

The transition of electron that gives rise to the formation of the second spectral line of the Balmer series in the spectrum of hydrogen atom corresponds to :

An electron makes a transition from orbit n = 2 to orbit n = 1, in Bohr’s model of hydrogen atom. Consider change in magnitudes of its kinetic energy (K) and potential energy (U).

The radius \(\left(r_n\right)\) of \(n^{\text {th }}\) orbit in Bohr model of hydrogen atom varies with \(n\) as

The energy of an electron in the ground state of hydrogen atom is -13.6 eV . The kinetic and potential energy of the electron in the first excited state will be

In Balmer series of hydrogen atom, as the wavelength of spectral lines decreases, they appear

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;

An electron makes a transition from orbit n = 2 to orbit n = 1, in Bohr’s model of hydrogen atom. Consider change in magnitudes of its kinetic energy (K) and potential energy (U).

In Balmer series of hydrogen atom, as the wavelength of spectral lines decreases, they appear

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)

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)]

The radius \(\left(r_n\right)\) of \(n^{\text {th }}\) orbit in Bohr model of hydrogen atom varies with \(n\) as

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

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)]

A proton and an alpha particle having equal velocities approach a target nucleus. They come momentarily to rest and then reverse their directions. The ratio of the distance of closest approach of the proton to that of the alpha particle will be :

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.

Energy levels A, B and C of an atom correspond to increasing values of energy i.e. \({\mathrm{E}}_{\mathrm{A}}<{\mathrm{E}}_{\mathrm{B}}<{\mathrm{E}}_{\mathrm{C}}\). Let \({\lambda }_{1},{\lambda }_{2}\) and \({\lambda }_{3}\) be the wavelengths of radiation corresponding to the transitions C to \(\mathrm{B}, \mathrm{B}\) to A and C to A , respectively. The correct relation between \({\lambda }_{1},{\lambda }_{2}\) and \({\lambda }_{3}\) is :

The transition of electron that gives rise to the formation of the second spectral line of the Balmer series in the spectrum of hydrogen atom corresponds to :

An electron makes a transition from \(n=2\) level to \(n=1\) level in the Bohr model of a hydrogen atom. Its period of revolution :

Which of the following statements is correct for alpha particle scattering experiment?

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

The radius \(\left(r_n\right)\) of \(n^{\text {th }}\) orbit in Bohr model of hydrogen atom varies with \(n\) as

The potential energy of an electron in the second excited state in hydrogen atom is :

An alpha particle approaches a gold nucleus in Geiger-Marsden experiment with kinetic energy K. It momentarily stops at a distance \(d\) from the nucleus and reverses its direction. Then d is proportional to :

Energy levels A, B and C of an atom correspond to increasing values of energy i.e. \({\mathrm{E}}_{\mathrm{A}}<{\mathrm{E}}_{\mathrm{B}}<{\mathrm{E}}_{\mathrm{C}}\). Let \({\lambda }_{1},{\lambda }_{2}\) and \({\lambda }_{3}\) be the wavelengths of radiation corresponding to the transitions C to \(\mathrm{B}, \mathrm{B}\) to A and C to A , respectively. The correct relation between \({\lambda }_{1},{\lambda }_{2}\) and \({\lambda }_{3}\) is :

The energy of an electron in the ground state of hydrogen atom is -13.6 eV . The kinetic and potential energy of the electron in the first excited state will be

The energy of an electron in the ground state of hydrogen atom is -13.6 eV . The kinetic and potential energy of the electron in the first excited state will be

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 :

An alpha particle approaches a gold nucleus in Geiger-Marsden experiment with kinetic energy K. It momentarily stops at a distance \(d\) from the nucleus and reverses its direction. Then d is proportional to :

In Balmer series of hydrogen atom, as the wavelength of spectral lines decreases, they appear

The transition of electron that gives rise to the formation of the second spectral line of the Balmer series in the spectrum of hydrogen atom corresponds to :

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)

An electron makes a transition from \(n=2\) level to \(n=1\) level in the Bohr model of a hydrogen atom. Its period of revolution :

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)

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)

The radius of the \(\mathrm{n}^{\text {th }}\) orbit in Bohr model of hydrogen atom is proportional to

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

The transition of electron that gives rise to the formation of the second spectral line of the Balmer series in the spectrum of hydrogen atom corresponds to :

The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is:

The transition of electron that gives rise to the formation of the second spectral line of the Balmer series in the spectrum of hydrogen atom corresponds to :

Which of the following statements is correct for alpha particle scattering experiment?

The transition of electron that gives rise to the formation of the second spectral line of the Balmer series in the spectrum of hydrogen atom corresponds to :

The ratio of maximum frequency and minimum frequency of light emitted in Balmer series of hydrogen spectrum, in Bohr's model is :

Assertion (A) : The potential energy of an electron revolving in any stationary orbit in a hydrogen atom is positive.
Reason (R) : The total energy of a charged particle is always positive.

For which one of the following, Bohr model is not valid?

The total energy of an electron in the \( \mathrm{n}^{\text {th }} \) stationary orbit of the hydrogen atom can be obtained by.

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 \(\overset{\mathrm{o}}{\mathrm{A}}\). What is the maximum kinetic energy of the emitted photoelectron?

Assertion (A) : An alpha particle is moving towards a gold nucleus. The impact parameter is maximum for the scattering angle of \(180^\circ\).
Reason (R) : The impact parameter in an alpha particle scattering experiment does not depend upon the atomic number of the target nucleus.

Hydrogen atom initially in the ground state, absorbs a photon which excites it to \(n =5\) level. The wavelength of the photon is :

A hydrogen atom makes a transition from \(n =5\) to \(n =1\) orbit. The wavelength of photon emitted is \(\lambda\). The wavelength of photon emitted when it makes a transition from \(n =5\) to \(n =2\) orbit is

In hydrogen spectrum, the shortest wavelength in the Balmer series is \(\lambda\). The shortest wavelength in the Bracket series is :

The radius of the \(n ^{\text {th }}\) orbit in Bohr model of hydrogen atom is proportional to :

A particle of mass m is moving around the origin with a constant force F pulling it towards the origin. If Bohr model is used to describe its motion, the radius of the \({\mathrm{n}}^{\text{th }}\) orbit and the particle's speed v in the orbit depend on n as

The energy required to break one bond in DNA is \( 10^{-20} \mathrm{~J} \). This value in \( \mathrm{eV} \) is nearly.

The radius of inner most orbit of hydrogen atom is \(5.3 \times 10^{-11} \mathrm{~m}\). What is the radius of third allowed orbit of hydrogen atom?