Atomic Structure — JEE Main PYQs

Given below are two statements:

Statement I: When an electric discharge is passed through gaseous hydrogen, the hydrogen molecules dissociate and the energetically excited hydrogen atoms produce electromagnetic radiation of discrete frequencies.

Statement II: The frequency of s …

The energy required by electrons, present in the first Bohr orbit of hydrogen atom to be excited to second Bohr orbit is ____ $\mathrm{J}{\mathrm{mol}}^{-1}$.

Given : ${\mathrm{R}}_{\mathrm{H}}=2.18\times 10^{-11}\mathrm{ergs}$.

Consider the following spectral lines for atomic hydrogen:
A. First line of Paschen series
B. Second line of Balmer series
C. Third line of Paschen series
D. Fourth line of Bracket series

The correct arrangement of the above lines in ascending order of energy is:

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 :

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

Given,
(A) $\mathrm{n}=5,{\mathrm{m}}_1=-1$
(B) $\mathrm{n}=3,1=2,{\mathrm{m}}_1=-1,{\mathrm{m}}_{\mathrm{s}}=+\frac{1}{2}$

The maximum number of electron(s) in an atom that can have the quantum numbers as given in (A) and (B) respectively are :

Identify the INCORRECT statements from the following:
A. Notation ${}_{12}^{24}\mathrm{Mg}$ represents 24 protons and 12 neutrons.
B. Wavelength of a radiation of frequency $4.5\times 10^{15}{\mathrm{s}}^{-1}$ is $6.7\times 10^{-8}\mathrm{m}$.
C. One radiation has wave …

The work functions of two metals ( ${\mathrm{M}}_{\mathrm{A}}$ and ${\mathrm{M}}_{\mathrm{B}}$ ) 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 wo …

The hydrogen spectrum consists of several spectral lines in Lyman series $({\mathrm{L}}_1,{\mathrm{L}}_2,{\mathrm{L}}_3\dots .;{\mathrm{L}}_1$ has lowest energy among Lyman series). Similarly it consists of several spectral lines in Balmer series ( …

The wavelength of spectral line obtained in the spectrum of ${\mathrm{Li}}^{2+}$ ion, when the transition takes place between two levels whose sum is 4 and difference is 2, is

The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series.
($\mathrm{R}=$ Rydberg constant)

Figure 1. electron probability density for 2s orbital

Figure 2. wave function for 2s orbital

Which of the following point in Figure 2 most accurately represents the nodal surface as shown in Figure 1?

The wavelength of photon ' $A$ ' is 400 nm . The frequency of photon ' B ' is $10^{16}{\mathrm{s}}^{-1}$. The wave number of photon ' C ' is $10^4{\mathrm{cm}}^{-1}$. The correct order of energy of these photons is :

Two positively charged particles ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ have been accelerated across the same potential difference of 200 keV as shown below.

[Given mass of ${\mathrm{m}}_1=1$ amu and ${\mathrm{m}}_2=4$ amu]
The deBroglie wavelength of ${\mathrm{m}}_1$ will be x t …

What is the energy (in J atom${}^{-1}$) required for the following process?
${\mathrm{Li}}^{2+}(\mathrm{g})\to {\mathrm{Li}}^{3+}(\mathrm{g})+{\mathrm{e}}^{-}$
(Take the ionization energy for the H atom in the ground state as $2.18\times 10^{-18}{\mathrm{J}}^{-1}$ atom${}^{-1}$)

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 number 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. H (first orbit)
B. He⁺ (first orbit)
C. He⁺ (second orbit)
D. Li²⁺ (first orbit)
E. Be³⁺ (Second orbit)

Choose the correct answer from the options given below:

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

Arrange the following atomic orbitals of multi electron atoms in order of increasing energy.
(A) $\mathrm{n}=3,\ell =2,\mathrm{m}=+1$
(B) $n=4,\ell =0,m=0$
(C) $\mathrm{n}=6,\ell =1,\mathrm{m}=0$
(D) $\mathrm{n}=5,\ell =1,\mathrm{m}=+1$
(E) …

Identify the correct statements from the following :
A. Heisenberg uncertainty principle is applicable to electron.
B. The size of $2p_x$ orbital is less than the size of $3p_x$ orbital.
C. The energy of 2s orbital of H atom is equal to the energy of 2s orbital of Li.
D …

Which of the following statement(s) is/are true ?
(A) If two orbitals have the same value of ( $\mathrm{n}+l$ ), 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 …

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

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. ${\lambda }_1=2000$ Å
2. ${\lambda }_2=6000$ Å

The ratio of the energies of these two radiations $\left(\frac{{\mathrm{E}}_1}{{\mathrm{E}}_2}\right)$ is ____. (Nearest integer)

Radius of the first excited state of Helium ion is given as :
${\mathrm{a}}_0\to$ radius of first stationary state of hydrogen atom.

Given below are two statements :

Statement (I): A spectral line will be observed for a $2{\mathrm{p}}_{\mathrm{x}}\to 2{\mathrm{p}}_{\mathrm{y}}$ transition.

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

In th …

Niobium ( Nb ) and ruthenium ( Ru ) have " x " and "y" number of electrons in their respective 4 d orbitals. The value of $\mathrm{x}+\mathrm{y}$ is ____

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

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 …

In a multielectron atom, which of the following orbitals described by three quantum numbers with have same energy in absence of electric and magnetic fields?
A. $\mathrm{n}=1,1=0,{\mathrm{m}}_1=0$
B. $\mathrm{n}=2,1=0,{\mathrm{m}}_1=0$
C. $\mathrm{n}=2,1=1,{\mathrm{m}}_1=1$ …

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 state …

Given below are two statements about X-ray spectra of elements :

Statement (I) : A plot of $\sqrt{v}$ ( $v=$ frequency of X-rays emitted) vs atomic mass is a straight line.

Statement (II) : A plot of $\nu (\nu =$ frequency of X-rays emitted) vs atomic number is a straight line. I …

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

If ${\mathrm{a}}_0$ 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]

For hydrogen like species, which of the following graphs provides the most appropriate representation of E vs Z plot for a constant n ?
[E: Energy of the stationary state,
Z : atomic number, $\mathrm{n}=$ principal quantum number]

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 mome …

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) (see structure) is the boundary surface diagram of the $2{\mathrm{p}}_{\mathrm{x}}$ orbital.
(C) The + and - signs in the wave functi …

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

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

Which one of the following about an electron occupying the 1s orbital in a hydrogen atom is incorrect? (Bohr's radius is represented by ${\mathrm{a}}_0$ )

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 electr …

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

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 …

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 $p_z$ orbital
C. The last electron goes to orbital with $n=2$ and $l=1$

1. The sum …

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)

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

The de-Broglie's wavelength of an electron in the 4th orbit is ____ πa₀. (a₀ = Bohr's radius)

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

The incorrect postulates of the Dalton's atomic theory are :
(A) Atoms of different elements differ in mass.
(B) Matter consists of divisible atoms.
(C) Compounds are formed when atoms of different element combine in a fixed ratio.
(D) All the atoms of given element have differen …