Structure of Atom

The maximum number of orbitals which can be identified with \(\mathrm{n}=4\) and \({m}_{l}=0\) is _______

Correct statements for an element with atomic number 9 are
(A). There can be 5 electrons for which \({\mathrm{m}}_{\mathrm{s}}=+\frac{1}{2}\) and 4 electrons for which \({\mathrm{m}}_{\mathrm{s}}=-\frac{1}{2}\)
(B). There is only one electron in \({p}_{z}\)orbital
(C). The last electron goes to orbital with \(\mathrm{n}=2\) and \(l=1\)
(D). The sum of angular nodes of all the atomic orbitals is 1 .

Choose the correct answer from the options given below:

A photon of wavelength 3000 \(\overset{^\circ }{\mathrm{A}}\) strikes a metal surface. The work function of the metal is 2.13 eV. What is the kinetic energy of the emitted photoelectron?
(h = 6.626 × \({10}^{-34}\) Js)

A photon of wavelength 3000 \(\overset{^\circ }{\mathrm{A}}\) strikes a metal surface. The work function of the metal is 2.13 eV. What is the kinetic energy of the emitted photoelectron?
(h = 6.626 × \({10}^{-34}\) Js)

The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series.

(R = Rydberg constant)

[JEE Main 2026, 28 Jan (Shift 1)]

The work functions of two metals (M_A and M_B) are in the 1 : 2 ratio. When these metals are exposed to photons of energy 6 eV, the kinetic energy of liberated electrons of M_A : M_B is in the ratio of 2.642 : 1. The work functions (in eV) of M_A and M_B are respectively.

[JEE Main 2026, 23 Jan (Shift 2)]

The energy of first (lowest) Balmer line of H atom is x J. The energy (in J) of second Balmer line of H atom is:

[JEE Main 2026, 22 Jan (Shift 2)]

Which of the following is/are not correct with respect to energy of atomic orbitals of hydrogen atom?
(A) 1s < 2p < 3d < 4s
(B) \(1s<2s=2p<3s=3p\)
(C) 1s < 2s < 2p < 3s < 3p
(D) \(1s<2s<4s<3d\)

Choose the correct answer from the options given below :

[JEE Main 2025, 28 Jan (Shift 2)]

A photon of wavelength 3000 \(\overset{^\circ }{\mathrm{A}}\) strikes a metal surface. The work function of the metal is 2.13 eV. What is the kinetic energy of the emitted photoelectron?
(h = 6.626 × \({10}^{-34}\) Js)

Which of the following energy order is correct for H-atoms?

Memory Based Question 28/Jan/25 Evening shift

The number of radial node/s for 3p orbital is:EndFragment

[JEE Main 2024, 01 Feb (Shift 2)]

According to Bohr's model, the highest kinetic energy is associated with the electron in the:

Match List I with List II

Choose the correct answer from the options given below :-

[JEE Main 2024, 29 Jan (Shift 2)]

Which of the following is/are not correct with respect to energy of atomic orbitals of hydrogen atom?
(A) 1s < 2p < 3d < 4s
(B) \(1s<2s=2p<3s=3p\)
(C) 1s < 2s < 2p < 3s < 3p
(D) \(1s<2s<4s<3d\)

Choose the correct answer from the options given below :

The correct order of energy of the following subshell is

1s, 2s, 3p, 3d

(Memory Based Question 28/Jan/25 Evening shift)

According to Bohr's model of hydrogen atom, which of the following statement is incorrect?

[JEE Main 2025, 2 Apr (Shift 1)]

In a multielectron atom, which of the following orbitals described by three quantum numbers will have same energy in absence of electric and magnetic fields?
A. \(n=1,1=0,{m}_{1}=0\)
B. \(n=2,1=0,{m}_{1}=0\)
C. \(n=2,1=1,{m}_{1}=1\)
D. \(n=3,1=2,{m}_{1}=1\)
E. \(n=3,1=2,{m}_{1}=0\)

Choose the correct answer from the options given below:

Which of the following has the same energy in the absence of electric and magnetic field for the hydrogen atom? (Memory-based Question 28/ Jan/25 morning shift )

Bohr's model is applicable for a single electron atom of atomic number Z. Dependency of frequency of rotation of electron in \({\mathrm{n}}^{\mathrm{th}}\) principal quantum number is proportional to (Memory Based Question 28/Jan/25 Evening shift)

The energy of first (lowest) Balmer line of H atom is x J. The energy (in J) of second Balmer line of H atom is:

[JEE Main 2026, 22 Jan (Shift 2)]

Compare the energies of following sets of quantum numbers for multielectron system
(A) \(\mathrm{n}=4,l=1\)
(B) \(\mathrm{n}=4,l=2\)
(C) \(\mathrm{n}=3,l=1\)
(D) \(\mathrm{n}=3,\mathrm{l}=2\)
(E) \(\mathrm{n}=4,l=0\)

Choose the correct answer from the options given below :

[JEE Main 2024, 9 Apr (Shift 1)]

If the de-Broglie wavelength of a particle of mass (m) is 100 times its velocity,

then its value in terms of its mass (m) and Planck constant (h) is:

The correct set of four quantum numbers for the valence electron of rubidium atom \((\mathrm{Z}=37)\) is :

The wavelength of spectral line obtained in the spectrum of Li²⁺ ion, when the transition takes place between two levels whose sum is 4 and difference is 2, is

For hydrogen atom, the orbital/s with lowest energy is/are :
(A) 4 s
(B) \(3{p}_{x}\)
(C) \(3{d}_{{x}^{2}-{y}^{2}}\)
(D) \(3{d}_{{z}^{2}}\)
(E) \(4{p}_{z}\)

Choose the correct answer from the options given below :

The wavelength of photon ‘A’ is 400 nm. The frequency photon ‘B’ is 10¹⁶ s^–1. The wave number of photon ‘C’ is 10⁴ cm^–1. The correct order energy of these photons is:

[JEE Main 2026, 28 Jan (Shift 2)]

For electron in ' 2s ' and ' 2p ' orbitals, the orbital angular momentum values, respectively are :

[JEE Main 2025, 3 Apr (Shift 2)]

According to Bohr's model, the highest kinetic energy is associated with the electron in the:

[JEE Advanced 2024, Paper-2]

The wavelength of photon ‘A’ is 400 nm. The frequency photon ‘B’ is 10¹⁶ s^–1. The wave number of photon ‘C’ is 10⁴ cm^–1. The correct order energy of these photons is:

[JEE Main 2026, 28 Jan (Shift 2)]

When light of wavelength \( 248 \mathrm{~nm} \) falls on a metal of threshold energy \( 3.0 \mathrm{~eV} \), the de-Broglie wavelength of emitted electrons is ....... Å.

[Use: \( \sqrt{3}=1.73, \mathrm{~h}=6.63 \times 10^{-34} \mathrm{Js}, \mathrm{m}_{\mathrm{e}}=9.1 \times 10^{-31} \mathrm{~kg} \); \( \left.\mathrm{c}=3.0 \times 10^{8} \mathrm{~ms}^{-1} ; 1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}\right] \)

[JEE Main 2021, 16 Mar (Shift 1)]

The extra stability of half-filled subshell is due to
(A) Symmetrical distribution of electrons
(B) Smaller coulombic repulsion energy
(C) The presence of electrons with the same spin in non-degenerate orbitals
(D) Larger exchange energy
(E) Relatively smaller shielding of electrons by one another
Identify the correct statements

[JEE Main 2025, 7 Apr (Shift 2)]

Given below are two statements :
Statement (I): It is impossible to specify simultaneously with arbitrary precision, both the linear momentum and the position of a particle.
Statement (II): If the uncertainty in the measurement of position and uncertainty in measurement of momentum are equal for an electron, then the uncertainty in the measurement of velocity is \(⩾\sqrt{\frac{h}{\pi }}\times \frac{1}{2m}\).
In the light of the above statements, choose the correct answer from the options given below :

[JEE Main 2025, 29 Jan (Shift 2)]

The work functions of two metals (M_A and M_B) are in the 1 : 2 ratio. When these metals are exposed to photons of energy 6 eV, the kinetic energy of liberated electrons of M_A : M_B is in the ratio of 2.642 : 1. The work functions (in eV) of M_A and M_B are respectively.

[JEE Main 2026, 23 Jan (Shift 2)]

The correct order of energy of the following subshell is

1s, 2s, 3p, 3d

(Memory Based Question 28/Jan/25 Evening shift)

An electron of \({\mathrm{He}}^{+}\) is present in 3^rd excited state. Find its De-broglie wavelength.

Consider the ground state of chromium atom (Z = 24). How many electrons are with Azimuthal quantum number l = 1 and l = 2 respectively ?

Given below are two statements

Statement-I: For a given shell, the total number of allowed orbitals is given by \({\mathrm{n}}^{2}\)

Statement-II: For any subshell, the spatial orientation of the orbitals is given by −ℓ to +ℓ values including zero

In the light of above statements, choose the correct answer from the options given below

[JEE Main 2025, 23 Jan (Shift 2)]

In a multielectron atom, which of the following orbitals described by three quantum numbers will have same energy in absence of electric and magnetic fields?
A. \(n=1,1=0,{m}_{1}=0\)
B. \(n=2,1=0,{m}_{1}=0\)
C. \(n=2,1=1,{m}_{1}=1\)
D. \(n=3,1=2,{m}_{1}=1\)
E. \(n=3,1=2,{m}_{1}=0\)

Choose the correct answer from the options given below:

[JEE Main 2025, 28 January (Shift 1)]

Given below are two statements :
Statement (I): It is impossible to specify simultaneously with arbitrary precision, both the linear momentum and the position of a particle.
Statement (II): If the uncertainty in the measurement of position and uncertainty in measurement of momentum are equal for an electron, then the uncertainty in the measurement of velocity is \(⩾\sqrt{\frac{h}{\pi }}\times \frac{1}{2m}\).
In the light of the above statements, choose the correct answer from the options given below :

For hydrogen atom, the orbital/s with lowest energy is/are :
(A) 4 s
(B) \(3{p}_{x}\)
(C) \(3{d}_{{x}^{2}-{y}^{2}}\)
(D) \(3{d}_{{z}^{2}}\)
(E) \(4{p}_{z}\)

Choose the correct answer from the options given below :

According to Bohr's model of hydrogen atom, which of the following statement is incorrect?

[JEE Main 2025, 2 Apr (Shift 1)]

Which of the following postulate of Bohr's model of hydrogen atom is not in agreement with quantum mechanical model of an atom ?

[JEE Main 2025, 3 Apr (Shift 1)]

Bohr's model is applicable for a single electron atom of atomic number Z. Dependency of frequency of rotation of electron in \({\mathrm{n}}^{\mathrm{th}}\) principal quantum number is proportional to (Memory Based Question 28/Jan/25 Evening shift)

Which of the following energy order is correct for H-atoms?

Memory Based Question 28/Jan/25 Evening shift

Given below are two statements

Statement-I: For a given shell, the total number of allowed orbitals is given by \({\mathrm{n}}^{2}\)

Statement-II: For any subshell, the spatial orientation of the orbitals is given by −ℓ to +ℓ values including zero

In the light of above statements, choose the correct answer from the options given below.

[JEE Main 2025, 23 Jan (Shift 2)]

An electron of \({\mathrm{He}}^{+}\) is present in 3^rd excited state. Find its De-broglie wavelength.

Given below are two statements

Statement-I: For a given shell, the total number of allowed orbitals is given by \({\mathrm{n}}^{2}\)

Statement-II: For any subshell, the spatial orientation of the orbitals is given by −ℓ to +ℓ values including zero

In the light of above statements, choose the correct answer from the options given below

[JEE Main 2025, 23 Jan (Shift 2)]

Identify the INCORRECT statements from the following:

A. Notation \({\text{​}}_{12}^{24}\text{Mg}\) represents 24 protons and 12 neutrons.

B. Wavelength of a radiation of frequency 4.5×10¹⁵ s^–1 is 6.7×10^–8 m.

C. One radiation has wavelength = λ₁ (900 nm) and energy = E₁. Other radiation has wavelength = λ₂ (300 nm) and energy = E₂. E₁ : E₂ = 3 : 1.

D. Number of photons of light of wavelength 2000 pm that provides 1 J of energy is 1.006×10¹⁶. Choose the correct answer from the given below:

[JEE Main 2026, 23 Jan (Shift 2)]

The four quantum numbers for the electron in the outer most orbital of potassium (atomic no. 19) are

[JEE Main 2024, 31 Jan (Shift 2)]

Which of the following has the same energy in the absence of electric and magnetic field for the hydrogen atom? (Memory-based Question 28/ Jan/25 morning shift )

The correct set of four quantum numbers for the valence electron of rubidium atom \((\mathrm{Z}=37)\) is :

[JEE Main 2024, 29 January (Shift 1)]

The energy of an electron in first Bohr orbit of H -atom is \(-13.6\mathrm{eV}\) . The magnitude of energy value of electron in the first excited state of \({\mathrm{Be}}^{3+}\) is _______eV . (nearest integer value)

[JEE Main 2025, 8 Apr (Shift 1)]

Heat treatment of muscular pain involves radiation of a wavelength of about 900 nm. Which spectral line of the H atom is suitable for this?

(Rydberg constant \({\mathrm{R}}_{\mathrm{H}}={10}^{5}{\mathrm{cm}}^{-1},\mathrm{h}=6.6\times {10}^{-34}\mathrm{Js},\mathrm{c}=3\times {10}^{8}\mathrm{m}/\mathrm{s}\))

[JEE Main 2025, 23 Jan (Shift 1)]

Given below are two statements :

Statement (I) : A spectral line will be observed for a 2p_x → 2p_y transition.

Statement (II) : \(2{\mathrm{p}}_{\mathrm{x}}\mathrm{and}2{\mathrm{p}}_{\mathrm{y}}\)are degenerate orbitals.

In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements :

Statement (I) : A spectral line will be observed for a 2p_x → 2p_y transition.

Statement (II) : \(2{\mathrm{p}}_{\mathrm{x}}\mathrm{and}2{\mathrm{p}}_{\mathrm{y}}\)are degenerate orbitals.

In the light of the above statements, choose the correct answer from the options given below :

[JEE Main 2025, 22 Jan (Shift 2)]

For hydrogen atom, energy of an electron in first excited state is \(-3.4 eV , K . E\). of the same electron of hydrogen atom is \(x eV\). Value of \(x\) is ......................\(\times 10^{-1} eV\). (Nearest integer)

[JEE Main 2024, 06 Apr (Shift 2)]

For hydrogen atom, energy of an electron in first excited state is \(-3.4 eV , K . E\). of the same electron of hydrogen atom is \(x eV\). Value of \(x\) is ......................\(\times 10^{-1} eV\). (Nearest integer)

[JEE Main 2024, 06 Apr (Shift 2)]

Which of the following sets of quantum numbers have the same energy? (Memory-based Question 28/ Jan/25 morning shift )

(a) n=2 , l=2 , m=+1

(a) n=2 , l=1 , m=-1

(a) n=3, l=2 , m=0

(a) n=3 , l=2 , m=1

If \({a}_{0}\) is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength \((\lambda )\) of the electron present in the second orbit of hydrogen atom?

The wavelength of spectral line obtained in the spectrum of Li²⁺ ion, when the transition takes place between two levels whose sum is 4 and difference is 2, is

[JEE Main 2026, 24 January (Shift 2)]

Identify the INCORRECT statements from the following:

A. Notation \({\text{​}}_{12}^{24}\text{Mg}\) represents 24 protons and 12 neutrons.

B. Wavelength of a radiation of frequency 4.5×10¹⁵ s^–1 is 6.7×10^–8 m.

C. One radiation has wavelength = λ₁ (900 nm) and energy = E₁. Other radiation has wavelength = λ₂ (300 nm) and energy = E₂. E₁ : E₂ = 3 : 1.

D. Number of photons of light of wavelength 2000 pm that provides 1 J of energy is 1.006×10¹⁶. Choose the correct answer from the given below:

[JEE Main 2026, 23 Jan (Shift 2)]

If the de-Broglie wavelength of a particle of mass (m) is 100 times its velocity,

then its value in terms of its mass (m) and Planck constant (h) is:

Which of the following sets of quantum numbers have the same energy? (Memory-based Question 28/ Jan/25 morning shift )

(a) n=2 , l=2 , m=+1

(a) n=2 , l=1 , m=-1

(a) n=3, l=2 , m=0

(a) n=3 , l=2 , m=1

In an atom, total number of electrons having quantum number \(\mathrm{n}=4,\left|{\mathrm{m}}_{\mathrm{l}}\right|=1,{\mathrm{m}}_{\mathrm{s}}=-\frac{1}{2}\) is ..............

Radius of electron in ground state for hydrogen is \({a}_{o}\), then radius of electron in \({\mathrm{He}}^{+}\)ion in \({3}^{\mathrm{rd}}\) excited state is a. Then \(\frac{{\mathrm{a}}_{\mathrm{o}}}{\mathrm{a}}\) is:

(Memory Based JEE Mains 22/01/2025,Shift -1)

If radius of the first Bohr orbit of H-atom is \({\mathrm{a}}_{\mathrm{o}}\), then find the radius of 2nd Bohr's orbit of H-atom (memory based jee mains shift-1 29/01/2025)

Heat treatment of muscular pain involves radiation of a wavelength of about 900 nm. Which spectral line of the H atom is suitable for this?

(Rydberg constant \({\mathrm{R}}_{\mathrm{H}}={10}^{5}{\mathrm{cm}}^{-1},\mathrm{h}=6.6\times {10}^{-34}\mathrm{Js},\mathrm{c}=3\times {10}^{8}\mathrm{m}/\mathrm{s}\))

[JEE Main 2025, 23 Jan (Shift 1)]

Which of the following statements regarding the energy of the stationary state is true in the following one-electron systems?

[JEE Main 2026, 23 Jan (Shift 1)]

Which of the following postulate of Bohr's model of hydrogen atom is not in agreement with quantum mechanical model of an atom ?

[JEE Main 2025, 3 Apr (Shift 1)]

Correct statements for an element with atomic number 9 are
(A). There can be 5 electrons for which \({\mathrm{m}}_{\mathrm{s}}=+\frac{1}{2}\) and 4 electrons for which \({\mathrm{m}}_{\mathrm{s}}=-\frac{1}{2}\)
(B). There is only one electron in \({p}_{z}\)orbital
(C). The last electron goes to orbital with \(\mathrm{n}=2\) and \(l=1\)
(D). The sum of angular nodes of all the atomic orbitals is 1 .

Choose the correct answer from the options given below:

[JEE Main 2025, 8 Apr (Shift 1)]

If \({a}_{0}\) is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength \((\lambda )\) of the electron present in the second orbit of hydrogen atom? [n : any integer]

[JEE Main 2025, 29 Jan (Shift 1)]

The energy required by electrons, present in the first Bohr orbit of hydrogen atom to be excited to second Bohr orbit is ____J mol^–1.

(Given: \({\text{R}}_{\text{H}}=2.18\times {10}^{−11}\) ergs)

[JEE Main 2026, 22 Jan (Shift 1)]

Which of the following statements regarding the energy of the stationary state is true in the following one-electron systems?

[JEE Main 2026, 23 Jan (Shift 1)]

The energy required by electrons, present in the first Bohr orbit of hydrogen atom to be excited to second Bohr orbit is ____J mol^–1.

(Given: \({\text{R}}_{\text{H}}=2.18\times {10}^{−11}\) ergs)

[JEE Main 2026, 22 Jan (Shift 1)]

For electron in ' 2s ' and ' 2p ' orbitals, the orbital angular momentum values, respectively are :

[JEE Main 2025, 3 Apr (Shift 2)]

Consider the ground state of chromium atom (Z = 24). How many electrons are with Azimuthal quantum number l = 1 and l = 2 respectively ?

Radius of the first excited state of Helium ion is given as : \({a}_{0}\to\) radius of first stationary state of hydrogen atom

[JEE Main 2025, 22 Jan (Shift 1)]

The correct order of energy of the following subshell is

1s, 2s, 3p, 3d

(Memory Based Question 28/Jan/25 Evening shift)

The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series.

(R = Rydberg constant)

[JEE Main 2026, 28 Jan (Shift 1)]

Radius of the first excited state of Helium ion is given as : \({a}_{0}\to\) radius of first stationary state of hydrogen atom

[JEE Main 2025, 22 Jan (Shift 1)]

The four quantum numbers for the electron in the outer most orbital of potassium (atomic no. 19) are

The extra stability of half-filled subshell is due to
(A) Symmetrical distribution of electrons
(B) Smaller coulombic repulsion energy
(C) The presence of electrons with the same spin in non-degenerate orbitals
(D) Larger exchange energy
(E) Relatively smaller shielding of electrons by one another
Identify the correct statements

[JEE Main 2025, 7 Apr (Shift 2)]

Wavenumber for a radiation having \(5800\overset{\mathrm{o}}{\mathrm{A}}\) wavelength is \(x \times 10 ~cm ^{-1}\). The value of \(x\) is ........ (Integer answer)

[JEE Main 2024, 08 Apr (Shift 2)]

Wavenumber for a radiation having \(5800\overset{\mathrm{o}}{\mathrm{A}}\) wavelength is \(x \times 10 ~cm ^{-1}\). The value of \(x\) is ........ (Integer answer)

[JEE Main 2024, 08 Apr (Shift 2)]

The number of the following statement/s which is/are incorrect is ______

[JEE Main 2023, 8 Apr (Shift 1)]

The difference between the radii of \(3^{\text {rd }}\) and \(4^{\text {th }}\) orbits of \(\mathrm{Li}^{2+}\) is \(\Delta \mathrm{R}_1\). The difference between the radii of \(3^{\text {rd }}\) and \(4^{\text {th }}\) orbits of \(\mathrm{He}^{+}\)is \(\Delta \mathrm{R}_2\). Ratio \(\Delta \mathrm{R}_1: \Delta \mathrm{R}_2\) is :

[JEE Main 2020, 5Sep (Shift 1)]

A 50 watt bulb emits monochromatic red light of wavelength of \( 795 \mathrm{~nm} \). The number of photons emitted per second by the bulb is \( x \times 10^{20} \). The value of \( x \) is ____(Nearest integer)

[Given: \( h=6.63 \times 10^{-34} \mathrm{Js} \) and \( c=3.0 \times 10^{8} \mathrm{~ms}^{-1} \) ]

[JEE Main 2021, 1 Sep (Shift 2)]

The number of protons, neutrons and electrons in \( { }_{71}^{175} \mathrm{Lu} \), respectively, are:

Values of work function \(\left({\mathrm{W}}_{0}\right)\) for a few metals are given below:

$$\begin{array}{|c|c|c|c|c|c|c|}\hline \text { Metal } & \mathrm{Li} & \mathrm{Na} & \mathrm{K} & \mathrm{Mg} & \mathrm{Cu} & \mathrm{Ag} \\\hline \mathrm{W}_0 / \mathrm{eV} & 2.42 & 2.3 & 2.25 & 3.7 & 4.8 & 4.3 \\\hline\end{array}$$

The number of metals which will show photoelectric effect when light of wavelength \(400\mathrm{nm}\) falls on it is_________

Given: \(\mathrm{h}=6.6\times {10}^{-34}\mathrm{J}\mathrm{s}\)

\(c=3\times {10}^{8}{\mathrm{ms}}^{-1};\mathrm{e}=1.6\times {10}^{-19}\mathrm{C}\)

Assume that the radius of the first Bohr orbit of hydrogen atom is 0.6 Angstroms. The radius of the third Bohr orbit of \({\mathrm{He}}^{+}\)is_________picometer. (Nearest Integer)

[JEE Main 2023, 29 Jan (Shift 2)]

The Bohr orbit radius for the hydrogen atom (n = 1) is approximately 0.530Å. The radius for the first excited state (n = 2) orbit is (in Å )

The frequency of radiation emitted when the electron falls from n = 4 to n = 1 in a hydrogen atom will be (Given : ionization energy of \(\mathrm{H}=2.18\times {10}^{-18}\mathrm{J}/\mathrm{atom}\mathrm{and}\mathrm{h}=6.625\times {10}^{-34}\mathrm{Js}\))

A source of monochromatic radiation of wavelength \( 400 \mathrm{~nm} \) provides \( 1000 \mathrm{~J} \) of energy in 10 seconds. When this radiation falls on the surface of sodium, \( \mathrm{x} \times 10^{20} \) electrons are ejected per second. Assume that wavelength \( 400 \mathrm{~nm} \) is sufficient for ejection of electron from the surface of sodium metal. The value of \( \mathrm{x} \) is ........ \( \left(\mathrm{h}=6.626 \times 10^{-34} \mathrm{Js}\right) \)

[JEE Main 2021, 25 Jul (Shift 1)]

A ball weighing \(10 \mathrm{~g}\) is moving with a velocity of \(90 \mathrm{~ms}^{-1}\). If the uncertainty in its velocity is \(5 \%\), then the uncertainty in its position is ______ \(\times 10^{-33} \mathrm{~m}\). (Rounded off to the nearest integer)
\(\text { [Given : } \mathrm{h}=6.63 \times 10^{-34} \mathrm{~Js} \text { ] }\)

[JEE Main 2021, 26 Feb (Shift 2)]

According to Bohrs atomic theory

(I) Kinetic enertgy of electron is \( \propto \frac{\mathrm{Z}^{2}}{\mathrm{n}^{2}} \).

(II) The product of velocity (v) of electron and principal quantum number \( (\mathrm{n}) \), \( v n \) \( \propto Z^{2} \).

(III) Frequency of revolution of electron in an orbit is \( \propto \frac{Z^{3}}{n^{3}} \).

(IV) Coulombic force of attraction on the electron is \( \propto \frac{Z^{3}}{n^{4}} \).

Choose the most appropriate answer the from the options given below

The total number of isoelectronic species from the given set is

\({\mathrm{O}}^{2-},{\mathrm{F}}^{-},\mathrm{Al},{\mathrm{Mg}}^{2+},{\mathrm{Na}}^{+},{\mathrm{O}}^{+},{\mathrm{Mg}}^{+},{\mathrm{Al}}^{3+},\mathrm{F}\)

[JEE Main 2023, 15 Apr (Shift 1)]

According to Bohrs atomic theory

(I) Kinetic enertgy of electron is \( \propto \frac{\mathrm{Z}^{2}}{\mathrm{n}^{2}} \).

(II) The product of velocity (v) of electron and principal quantum number \( (\mathrm{n}) \), \( v n \) \( \propto Z^{2} \).

(III) Frequency of revolution of electron in an orbit is \( \propto \frac{Z^{3}}{n^{3}} \).

(IV) Coulombic force of attraction on the electron is \( \propto \frac{Z^{3}}{n^{4}} \).

Choose the most appropriate answer the from options given below

For \({\mathrm{He}}^{+}\), a transition takes place from the orbit of radius \(105.8 \mathrm{~pm}\) to the orbit of radius \(26.45 \mathrm{~pm}\). The wavelength (in nm ) of the emitted photon during the transition is _____

[Use: Bohr radius, \(\mathrm{a}=52.9\mathrm{pm}\)

Rydberg constant, \({\mathrm{R}}_{\mathrm{H}}=2.2\times {10}^{-18}\mathrm{J}\)

Planck's constant, \(\mathrm{h}=6.6\times {10}^{-34}\mathrm{J}\mathrm{s}\)

Speed of light, \(\mathrm{c}=3\times {10}^{8}\mathrm{m}{\mathrm{s}}^{-1}\)]

[JEE Advanced 2023, Paper-2]

\( \mathrm{Ge}(Z=32) \) in its ground state electronic configuration has x completely filled orbitals with \( \mathrm{m}_{l}=0 \). The value of \( \mathrm{x} \) is ?

[JEE Main 2021, 31 Aug (Shift 1)]

Given below are two statements:

Statement I: Bohr’s theory accounts for the stability and line spectrum of Li⁺ ion.

Statement II: Bohr’s theory was unable to explain the splitting of spectral lines in the presence of a magnetic field.

In the light of the above statements, choose the most appropriate answer from the options given below.

[JEE Main 2021, 18 Mar (Shift 2)]

Given below are the quantum numbers for 4 electrons.
A. \(\mathrm{n}=3,ℓ=2,{\mathrm{m}}_{ℓ}=1,{\mathrm{m}}_{\mathrm{s}}=+1/2\)
B. \(\mathrm{n}=4,ℓ=1,{\mathrm{m}}_{ℓ}=0,{\mathrm{m}}_{\mathrm{s}}=+1/2\)
C. \(\mathrm{n}=4,ℓ=2,{\mathrm{m}}_{ℓ}=-2,{\mathrm{m}}_{\mathrm{s}}=-1/2\)
D. \(\mathrm{n}=3,ℓ=1,{\mathrm{m}}_{ℓ}=-1,{\mathrm{m}}_{\mathrm{s}}=+1/2\)

The correct order of increasing energy is

[JEE Main 2022, 29 Jul (Shift 2)]

Arrange the following orbitals in decreasing order of energy.

A. \( \mathrm{n}=3, l=0, \mathrm{~m}=0 \)

B. \( \mathrm{n}=4, l=0, \mathrm{~m}=0 \)

C. \( \mathrm{n}=3, l=1, \mathrm{~m}=0 \)

D. \( \mathrm{n}=3, l=2, \mathrm{~m}=1 \)

The correct option for the order is

[JEE Main 2023, 31 Jan (Shift 2)]

Given below are two statements:

Statement-I: Bohr's theory accounts for the stability and line spectrum of \(\mathrm{Li}^{+}\) ion.

Statement-II: Bohr's theory was unable to explain the splitting of spectral lines in the presence of a magnetic field.

In the light of the above statements, choose the most appropriate answer from the options given below:

[JEE Main 2021, 18 March (Shift 2)]

Electrons in a cathode ray tube have been emitted with a velocity of \(1000{\mathrm{ms}}^{-1}\). The number of following statements which is/are true about the emitted radiation is________.

Given : \(\mathrm{h}=6\times {10}^{-34}\mathrm{Js},{\mathrm{m}}_{\mathrm{e}}=9\times {10}^{-31}\mathrm{kg}\).

(a)The deBroglie wavelength of the electron emitted is 666.67 nm

(b) The characteristic of electrons emitted depend upon the material of the electrodes of the cathode ray tube

(c) The cathode rays start from cathode and move towards anode

(d) The nature of the emitted electrons depends on the nature of the gas present in cathode ray tube

[JEE Main 2023, 1 Feb (Shift 1)]

The orbital having two radial as well as two angular nodes is :

Which transition in the hydrogen spectrum would have the same wavelength as the Balmer type transition from \(n=4\) to \(n=2\) of \({\mathrm{He}}^{+}\) spectrum?

[JEE Main 2023, 31 Jan (Shift 1)]

The number of atomic orbitals from the following \(7\mathrm{s},7\mathrm{p},6\mathrm{s},8\mathrm{p},8\mathrm{d}\)having 5 radial node is-

[JEE Main 2023, 8 April (Shift 2)]

If the radius of the first orbit of hydrogen atom is a₀, then de Broglie’s wavelength of electron in 3rd orbit is