JEE Advanced Previous Year Questions (2018 - 2023): Structure of Atom | Chemistry for JEE Main & Advanced PDF Download

2023

where r is in pm, n is the principal quantum number, and Z is the atomic number.
2. For a He⁺ ion, Z = 2.
3. We are given the initial radius r₂=105.8 pm and the final radius r₁=26.45 pm.
4. We can substitute these radii into the equation for r to find the corresponding quantum numbers.
For r₂ = 105.8 pm, we get :

which gives n₂ = 2.
Similarly, for r₁ = 26.45 pm, we get :

which gives n₁ = 1.
5. Therefore, the transition is from n₂ = 2 to n₁ = 1.
6. The energy difference during this transition is equal to the energy of the emitted photon, which is given by :

where ℎ is the Planck's constant, c is the speed of light, R_H is the Rydberg constant, and λ is the wavelength of the photon.
7. Substituting all known values into this equation gives :

Solving this equation yields λ = 30 × 10⁻⁹ m, or 30 nm.
8. So, the wavelength of the emitted photon during the transition is 30 nm. 

2022

Option (A) is correct.

Option (B) is incorrect.

π^∗ orbital has zero node is the plane which is perpendicular to the molecular axis and goes through the center of molecule.

So, option (C) is incorrect.

π^∗ Orbital has one node in the xy− plane containing the molecular axis.
Option (D) is correct.

2021

=
Velocity, = V cm/s.
Using de-Broglie equation,

= 30 cm/s

2020

Ans: − 5242.41
Given that, electrons and nucleus are at infinite distance, so potential energy of H-atom is taken as zero.
Therefore, according to Bohr's model, potential energy of a H-atom with electron in its ground state
= −27.2 eV
At d = d₀, nucleus-nucleus and electron-electron repulsion is absent.
Hence, potential energy will be calculated for 2 H atoms =  −2 × 27.2 eV = −54.4 eV
Potential energy of 1 mol H atoms in kJ

=

= − 5242.4192 KJ

2019

Q1: Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the nth orbit of the atom and List-II contains options showing how they depend on n. 

Which of the following options has the correct combination considering List-I and List-II?
(a) (III), (P)
(b) (III), (S)
(c) (IV), (U)
(d) (IV), (Q)                   [JEE Advanced 2019 Paper 2]
Ans: (a)
(III) Kinetic energy of the electron in nth orbit,

From List-II, correct match is (III, P)
(IV) Potential energy of the electron in the nth orbit,

From List-II, correct match is (IV, P).
Hence, correct matching from List-I and List-II on the basis of given options is (III, P).

Q2: Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the nth orbit of the atom and List-II contains options showing how they depend on n. 

Which of the following options has the correct combination considering List-I and List-II?
(a) (II), (R)
(b) (I), (P)
(c) (I), (T)
(d) (II), (Q)                   [JEE Advanced 2019 Paper 2]
Ans: (c)
(I) Radius of the nth orbit, r = 0.529 x n² / Z
Here, r ∝ n²
From List-II, correct match is (I, T)
(II) Angular momentum of the electron, 
From List - II, correct match (II, S)
Hence, correct matching from List-I and List-II on the basis of given options is (I, T).

Q3: The ground state energy of hydrogen atom is −13.6 eV. Consider an electronic state ψ of He⁺ whose energy, azimuthal quantum number and magnetic quantum number are −3.4 eV, 2 and 0, respectively.
Which of the following statement(s) is(are) true for the state ψ?
(a) It is a 4d state
(b) The nuclear charge experienced by the electron in this state is less than 2e, where e is the magnitude of the electronic charge
(c) It has 2 angular nodes
(d) It has 3 radial nodes    [JEE Advanced 2019 Paper 2]
Ans: (a) & (c)
Given, ground state energy of hydrogen atom = −13.6 eV
Energy of He⁺ = −3.4 eV, Z = 2
Energy of He⁺,

Given, azimuthal quantum number (l) = 2 (d − subshell)
Magnetic quantum number (m) = 0
∴ Angular nodes (l) = 2
Radial node = n − l − 1 = 4 − 2 − 1 = 1
nl = 4d state
Hence, options (a), (c) are correct.

Q4: Which of the following statement(s) is(are) correct regarding the root mean square speed (U_rms) and average translational kinetic energy (E_av) of a molecule in a gas at equilibrium?
(a) U_rms is inversely proportional to the square root of its molecular mass.
(b) U_rms is doubled when its temperature is increased four times.
(c) E_avg is doubled when its temperature is increased four times.
(d) E_avg at a given temperature does not depend on its molecular mass.  [JEE Advanced 2019 Paper 1]
Ans: (a), (b) & (d)
The explanation of given statements are as follows :
(a) U_rms is inversely proportional to the square root of its molecular mass.

Hence, option (a) is correct.
(b) When temperature is increased four times then U_rms become doubled.

Hence, option (b) is correct.
(c) and (d) E_av is directly proportional to temperature but does not depends on its molecular mass at a given temperature as . If temperature raised four times than E_av becomes four time multiple. 
Thus, option (c) is incorrect and option (d) is correct.