Atomic Structure Previous Year Questions with Solutions

The atomic structure consists of a nucleus at the center, containing protons (positively charged) and neutrons (neutral), with electrons (negatively charged) orbiting around it. The concept of atoms dates back to Democritus, who first suggested that matter is made of atoms. The study of atomic structure is crucial for understanding chemical reactions, bonds, and physical properties. John Dalton proposed the first scientific theory of atomic structure in the 1800s.

Studying atomic structure in previous years' questions with solutions for JEE Main Chemistry is crucial to understanding the question trends and identifying frequently asked topics like Bohr’s model, quantum numbers, Heisenberg uncertainty principle, etc. By practising atomic structure PYQs questions with solutions, aspirants can improve their problem-solving skills and increase their chances of scoring well in the JEE Main exam. 

1.0Key Concepts to Remember

Subatomic Particles

1. Protons: Positively charged particles located in the nucleus. The number of protons in an atom determines its atomic number, which identifies the element.
2. Neutrons: Neutral particles with a mass roughly equal to that of protons, also found in the nucleus. Neutrons play a key role in the atom's stability.
3. Electrons: Negatively charged particles with negligible mass compared to protons and neutrons. Electrons orbit the nucleus in discrete energy levels.

The atomic number of an element equals the number of protons in its nucleus, while the mass number is the sum of protons and neutrons. Atoms can gain or lose electrons, becoming ions with a net charge.

Atomic Models

Over the years, several atomic models were proposed to explain atomic structure:

1. Dalton's Model (1803): Proposed that atoms are indivisible and that chemical reactions involve the rearrangement of atoms. This model couldn’t explain the internal structure of atoms or the existence of isotopes.
2. Thomson’s Model (1897): Known as the "plum pudding model," it proposed that electrons are embedded in a positively charged sphere. This model was based on the discovery of the electron by J.J. Thomson but could not explain atomic stability.
3. Rutherford’s Model (1911): Based on the gold foil experiment, Rutherford suggested that atoms are mostly empty space with a dense, positively charged nucleus. Electrons orbit the nucleus, but this model couldn't explain why electrons don’t spiral into the nucleus due to energy loss.
4. Bohr's Model (1913): Niels Bohr proposed that electrons move in fixed orbits around the nucleus without radiating energy, explaining the hydrogen atom’s spectral lines. This model works well for hydrogen but fails for multi-electron atoms.

Quantum Numbers

Quantum mechanics provides a more accurate description of atomic structure. The state of an electron in an atom is described by quantum numbers:

1. Principal Quantum Number (n): Specifies the energy level or shell where the electron resides. The higher the value of n, the higher the energy level.
2. Azimuthal Quantum Number (l): Defines the shape of the orbital (s, p, d, f). lll can take values from 0 to n−1n-1n−1.
3. Magnetic Quantum Number (m): Determines the orientation of the orbital in space. It can take values from −l to +l
4. Spin Quantum Number (s): Describes the electron's spin direction (clockwise or counterclockwise), with values of ±1/2​.

Electronic Configuration

The arrangement of electrons in an atom is governed by the following principles:

1. Aufbau Principle: Electrons fill the lowest available energy levels first before occupying higher levels.
2. Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers.
3. Hund’s Rule: Electrons occupy degenerate orbitals (orbitals of the same energy) singly before pairing up.

The electronic configuration describes how electrons are distributed among orbitals in an atom. For example, the configuration for oxygen (atomic number 8) is 1s²2s²2p⁴

2.0JEE Main Past Year Questions with Solutions on Atomic Structure

Q. 1  According to the wave-particle duality of matter by de-Broglie, which of the following graph plots present the most appropriate relationship between the wavelength of electron (l) and momentum of electron (p)?

Ans. (1)

Solution:     

$\lambda =\frac{h}{p}\left[\lambda \propto \frac{1}{p}\right]$

l_p = h (constant)

So, the plot is a rectangular hyperbola.

Q.2  A hypothetical electromagnetic wave is shown below. 

The frequency of the wave is x × 10¹⁹ Hz.

x = ______ (nearest integer)

Ans.   (5)

Solution:  Correct answer is : 5 

𝜆 = 1.5 × 4 pm = 6 × 10⁻¹²meter     

λ _v = C

6 × 10⁻¹²meter × v = 3 × 10⁸ 

𝑣 = 5 × 10¹⁹ Hz

Q.3 The ionization energy of sodium in kJ mol^–1_. If electromagnetic radiation of wavelength 242 nm is just sufficient to ionize sodium atom is______.

Ans.   (494)

Solution:

$$\begin{gathered} E=\frac{1240}{\lambda (\text{nm})}\text{eV} \\ =\frac{1240}{242}\text{eV}=5.12\text{eV} \end{gathered}$$

= 5.12 eV

= 5.12 × 1.6 × 10^–19

= 8.198 × 10^–19 J/atom

= 494 kJ/mol

Q.4  The following figure shows the spectrum of an ideal black body at four different temperatures. The number of correct statement/s from the following is _______.

A.  T₄ > T₃ > T₂ > T₁

B.  The black body consists of particles performing simple harmonic motion.

C. The peak of the spectrum shifts to a shorter wavelength as temperature increases.

 D. $\frac{T_1}{{\nu }_1}=\frac{T_2}{{\nu }_2}=\frac{T_3}{{\nu }_3}$

E. The given spectrum could be explained using quantisation of energy

Solution: 

The spectrum of Black body radiation is explained using quantization of energy. With increase in temperature, the peak of the spectrum shifts to shorter wavelength or higher frequency. For above graph

$T_1<T_2<T_3<T_4.$

Q.5 Electrons in a cathode ray tube have been emitted with a velocity of 1000 ms^–1. The number of following statements which is/are true about the emitted radiation is _________.

Given: h = 6 × 10^–34 Js, m_e = 9 × 10^–31 kg.

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

(B)   The characteristic of electrons emitted depends upon the material of the electrodes of the cathode ray tube.

(C)   The cathode rays start from the cathode and move towards anode.

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

Solution: 

(A) V_e = 1000 m/s ; h = 6 × 10^–34 Js ;

m_e = 9 × 10^–31 kg

$I=\frac{h}{mv}=\frac{6\times 10^{-34}}{9\times 10^{-31}\times 1000}$

= 666.67 × 10^–9 m

= 666.67 nm

Q.6. The electron in the n^th orbit of Li²⁺ is excited to (n + 1) orbit using the radiation of energy 1.47 × 10^–17J (as shown in the diagram). The value of n is ________.

Given R_H = 2.18 × 10^–18J 

Solution: 

Given

$$\begin{gathered} R_H=2.18\times 10^{-18}J \\ \Delta E=R_H{Z}^2\left(\frac{1}{n^2}-\frac{1}{(n+1{)}^2}\right) \\ 1.47\times 10^{-17}=2.18\times 10^{-18}\times 9\left(\frac{1}{n^2}-\frac{1}{(n+1{)}^2}\right) \\ \frac{1.47}{1.96}=\left(\frac{1}{n^2}-\frac{1}{(n+1{)}^2}\right) \\ \Rightarrow \frac{3}{4}=\left(\frac{1}{n^2}-\frac{1}{(n+1{)}^2}\right) \\ \Rightarrow \boxed{n=1} \end{gathered}$$

Q.7 The spin-only magnetic moment value of M³⁺ ion (in gaseous state) from the pairs Cr³⁺/Cr²⁺, Mn³⁺/Mn², Fe³⁺/Fe²⁺ and Co³⁺/Co²⁺ that has negative standard electrode potential, is B.M. [Nearest integer]

Solution: 

$$\begin{gathered} E_{{\text{Cr}}^{3+}/{\text{Cr}}^{2+}}^{\circ }=-0.41\text{V} \\ {\text{Electronic configuration of Cr}}^{3+}=[\text{Ar}]3d^3 \\ \mu =\sqrt{n(n+2)}\text{B.M} \\ =\sqrt{3(3+2)}=\sqrt{15}\approx \boxed{4}\text{B.M} \\ \text{Answer:}\boxed{4B.M} \end{gathered}$$

Q.8 Match the List I with List- II.

Choose the most appropriate answer from the options given below:

(1) (A)-(I), (B)-(II), (C)-(III), (D)-(IV)

(2) (A)-(III), (B)-(II), (C)-(I), (D)-(IV)

(3) (A)-(III), (B)-(I), (C)-(II), (D)-(IV)

(4) (A)-(IV), (B)-(II), (C)-(I), (D)-(III)

Ans. 1

Solution: Option 1(NCERT Table 10.1.5)

Q.9  The minimum uncertainty in the speed of an electron in an one-dimensional region of length 2a₀ (Where a₀ = Bohr radius 52.9 pm) is _____km s^–1. (Given : Mass of electron = 9.l × 10^–31 kg, Planck's constant h = 6.63 × 10^–34 Js)

Solution: 

Heisenberg’s uncertainty principle

$$\begin{gathered} \Delta x\times \Delta p_x\ge \frac{h}{4\pi } \\ \Rightarrow 2a_0\times m\Delta v_x=\frac{h}{4\pi }\text{(minimum)} \\ \Rightarrow \Delta v_x=\frac{h}{4\pi }\times \frac{1}{2a_0}\times \frac{1}{m} \\ =\frac{6.63\times 10^{-34}}{4\times 3.14\times 2\times 52.9\times 10^{-12}\times 9.1\times 10^{-31}} \\ =548273{\text{ms}}^{-1} \\ =548.273{\text{km s}}^{-1} \\ =\boxed{548}{\text{km s}}^{-1} \end{gathered}$$

Q.10  The plots of radial distribution functions for various orbitals of hydrogen atom against 'r' are given below:

The correct plot for 3s orbital is:

(1) (B)   

(2) (A)    

(3) (D)    

(4) (C)

Solution: 

Number of radial nodes = n – l – 1

= 3 – 0 – 1 = 2

Therefore, corresponding graph is (D)         

Hence answer is option  (3)

Q.11 Electromagnetic radiation of wavelength 663 nm is just sufficient to ionise the atom of metal A. The ionization energy of metal A in kJ mol–1 is _______. (Rounded-off to the nearest integer)

[h = 6.63 × 10–34 Js, c = 3.00 × 108 ms–1,  NA = 6.02 × 1023 mol–1]

Solution: 

$$\begin{gathered} E=\frac{hc}{\lambda }\times \frac{N_A}{1000} \\ =\frac{6.63\times 10^{-34}\times 3\times 10^8\times 6.02\times 10^{23}}{663\times 10^{-9}\times 1000} \\ =3\times 6.02\times 10\text{kJ}=180.6\text{kJ} \end{gathered}$$

Q.12 Given below are two statements.

Statement I: According to Bohr's model of an atom, qualitatively the magnitude of the velocity of an electron increases with decrease in positive charges on the nucleus as there is no strong hold on the electron by the nucleus.

Statement II: According to Bohr's model of an atom, qualitatively the magnitude of the velocity of an electron increases with decrease in principal quantum number.

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

below:

(1) Both Statement I and Statement II are false

(2) Both Statement I and Statement II are true

(3) Statement I is false but Statement II is true

(4) Statement I is true but Statement II is false

Solution: 

Velocity of an electron in Bohr's atom is given by

$v\propto \frac{Z}{n}$

Z = the atomic number of an atom, which corresponds to +ve charge. As Z increases, velocity increases, so statement-I is wrong.`and as 'n' decreases velocity increases so statement II is correct.