Atomic Structure — JEE Main PYQs

The surface of sodium metal is irradiated with radiation of wavelength $x$ nm. The kinetic energy of ejected electrons is $2.8 \times 10^{-20}$ J. The work function of sodium is 2.3 eV. The value of $x$ is __________ $\times 10^{2}$ nm. (Nearest integer)

(Given : $h = 6.6 \times 10^{-34}$ J s ; 1 eV $= 1.6 \times 10^{-19}$ J; $c = 3.0 \times 10^{8}$ m s$^{-1}$)

What is the ratio of wave number of first line (lowest energy line) of Balmer series of H atomic spectrum to first line of its Brackett series?

Which of the following is correct set of 4 quantum numbers of $19^{\text{th}}$ electron in Chromium (Atomic number = 24) in accordance with Aufbau principle?

The species having identical radii according to the Bohr's theory are:

A. $\mathrm{H}$ (first orbit)

B. $\mathrm{He^+}$ (first orbit)

C. $\mathrm{He^+}$ (Second orbit)

D. $\mathrm{Li^{2+}}$ (first orbit)

E. $\mathrm{Be^{3+}}$ (Second orbit)

Choose the correct answer from the options given below:

Arrange the following atomic orbitals of multi electron atoms in order of increasing energy.

A. $n = 3,\ l = 2,\ m = +1$ B. $n = 4,\ l = 0,\ m = 0$ C. $n = 6,\ l = 1,\ m = 0$ D. $n = 5,\ l = 1,\ m = +1$ E. $n = 2,\ l = 1,\ m = +1$

Choose the correct answer from the options given below:

Identify the correct statements from the following :

A. Heisenberg uncertainty principle is applicable to electrons. B. The size of $\mathrm{2p_x}$ orbital is less than the size of $\mathrm{3p_x}$ orbital. C. The energy of 2s orbital of H atom is equal to the energy of 2s orbital of Li. D. The electronic configuration of Cr is $\mathrm{[Ar]\ 3d^5\ 4s^1}$

Choose the correct answer from the options given below:

Which of the following statement(s) is/are true?

A. If two orbitals have the same value of $(n+l)$, the orbital with lower value of $n$ will have lower energy.

B. Energies of the orbitals in the same subshell increase with increase in atomic number.

C. The size of $2p_x$ orbital is less than the size of $3p_x$ orbital.

D. Among 5f, 6s, 4d, 5p and 5d orbitals, none of the orbitals have 2 radial nodes.

Choose the correct answer from the options given below :

If shortest wavelength of hydrogen atom in Lyman series is $x$, then longest wavelength in Balmer series of $\mathrm{He^+}$ is:

Match the LIST-I with LIST-II

List-I (Orbital)	List-II (Radial nodes and nodal plane)
A. 2s	I. 1 Radial node + two nodal planes
B. 3s	II. 1 Radial node + one nodal plane
C. 3p	III. 2 Radial nodes + No nodal plane
D. 4d	IV. 1 Radial node + No nodal plane

Choose the correct answer from the options given below:

The Bohr radius of a hydrogen like species is 70.53 pm. The species and the stationary state (n) are respectively

(Given : Hydrogen atom Bohr radius is 52.9 pm)

Consider two radiations of wavelengths

1. $\lambda_1 = 2000\ \mathrm{\mathring{A}}$
2. $\lambda_2 = 6000\ \mathrm{\mathring{A}}$

The ratio of the energies of these two radiations $\left(\dfrac{\mathrm{E_1}}{\mathrm{E_2}}\right)$ is __________ (Nearest integer).

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

Which of the following statements are true ?

(A) The subsidiary quantum number $l$ describes the shape of the orbital occupied by the electron.

(B) [Figure: two lobes along the x-axis, dumbbell shape] is the boundary surface diagram of the $\mathrm{2p}_x$ orbital.

(C) The $+$ and $-$ signs in the wave function of the $\mathrm{2p}_x$ orbital refer to charge.

(D) The wave function of $\mathrm{2p}_x$ orbital is zero everywhere in the $xy$ plane.

Choose the correct answer from the options given below :

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

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

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

[Figure: visible spectrum strip labelled with wavelength $\lambda$ (nanometers) from 400 to 750 nm, showing violet through red]

Which of the following statements are correct, if the threshold frequency of caesium is $5.16 \times 10^{14}$ Hz?

A. When Cs is placed inside a vacuum chamber with an ammeter connected to it and yellow light is focused on Cs, the ammeter shows the presence of current. B. When the brightness of the yellow light is dimmed, the value of the current in the ammeter is reduced. C. When a red light is used instead of the yellow light, the current produced is higher with respect to the yellow light. D. When a blue light is used, the ammeter shows the formation of current. E. When a white light is used, the ammeter shows formation of current.

Choose the correct answer from the options given below:

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 :

Correct statements for an element with atomic number 9 are

A. There can be 5 electrons for which $m_s = +\frac{1}{2}$ and 4 electrons for which $m_s = -\frac{1}{2}$

B. There is only one electron in $\mathrm{p_z}$ orbital.

C. The last electron goes to orbital with $n = 2$ 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:

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

Radius of the first excited state of Helium ion is given as :

$a_0 \rightarrow$ radius of first stationary state of hydrogen atom.

Given below are two statements :

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

Statement (II) : $2p_x$ and $2p_y$ are degenerate orbitals.

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

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

Given : Rydberg constant $\mathrm{R_H} = 10^5\ \mathrm{cm^{-1}}$, $h = 6.6 \times 10^{-34}$ J s, $c = 3 \times 10^8$ m/s)

Given below are two statements :

Statement (I) : For a given shell, the total number of allowed orbitals is given by $n^2$.

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

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

For hydrogen atom, the orbital/s with lowest energy is/are :

(A) $\mathrm{4s}$ (B) $\mathrm{3p_x}$ (C) $\mathrm{3d_{x^2-y^2}}$ (D) $\mathrm{3d_{z^2}}$ (E) $\mathrm{4p_z}$

Choose the correct answer from the options given below :

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 de-Broglie's wavelength of an electron in the 4$^{th}$ orbit is ________ $\pi a_0$. ($a_0$ = Bohr's radius)

The maximum number of orbitals which can be identified with $n = 4$ and $m_l = 0$ is ________.

The value of Rydberg constant ($\mathrm{R_H}$) is $2.18 \times 10^{-18}$ J. The velocity of electron having mass $9.1 \times 10^{-31}$ kg in Bohr's first orbit of hydrogen atom $=$ ________ $\times 10^{5}~\mathrm{ms^{-1}}$ (nearest integer).

In an atom, total number of electrons having quantum numbers $n = 4$, $|m_l| = 1$ and $m_s = -\frac{1}{2}$ is ________.

Frequency of the de-Broglie wave of electron in Bohr's first orbit of hydrogen atom is __________ $\times 10^{13}$ Hz (nearest integer).

[Given : $\mathrm{R_H}$ (Rydberg constant) $= 2.18 \times 10^{-18}$ J, $h$ (Plank's constant) $= 6.6 \times 10^{-34}$ J.s.]

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)

A hypothetical electromagnetic wave is show below.

[Figure: sinusoidal wave; a horizontal span of 1.5 pm is marked from the start of the wave up to the first crest]

The frequency of the wave is $x \times 10^{19}$ Hz.

x = _________ (nearest integer)

Wavenumber for a radiation having 5800 $\mathrm{\AA}$ wavelength is $x \times 10\ \mathrm{cm^{-1}}$. The value of $x$ is ______. (Integer answer)

Compare the energies of following sets of quantum numbers for multielectron system. (A) $n = 4, l = 1$ (B) $n = 4, l = 2$ (C) $n = 3, l = 1$ (D) $n = 3, l = 2$ (E) $n = 4, l = 0$ Choose the correct answer from the options given below :

Based on Heisenberg's uncertainty principle, the uncertainty in the velocity of the electron to be found within an atomic nucleus of diameter $10^{-15}$ m is ________ $\times\ 10^{9}\ \mathrm{ms^{-1}}$ (nearest integer)

[Given : mass of electron $= 9.1 \times 10^{-31}$ kg, Plank's constant $(h) = 6.626 \times 10^{-34}$ Js] (Value of $\pi = 3.14$)

According to the wave-particle duality of matter by de-Broglie, which of the following graph plot presents most appropriate relationship between wavelength of electron($\lambda$) and momentum of electron (p) ?

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

The number of electrons present in all the completely filled subshells having $n = 4$ and $s = +\frac{1}{2}$ is ________.

(Where $n$ = principal quantum number and $s$ = spin quantum number)

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

Given below are two statements :

Statement (I) : The orbitals having same energy are called as degenerate orbitals.

Statement (II) : In hydrogen atom, 3p and 3d orbitals are not degenerate orbitals.

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

Number of spectral lines obtained in $\mathrm{He^+}$ spectra, when an electron makes transition from fifth excited state to first excited state will be

The ionization energy of sodium in $\mathrm{kJ\,mol^{-1}}$, if electromagnetic radiation of wavelength $242\,\mathrm{nm}$ is just sufficient to ionize sodium atom is _______.

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