Match the following rules with their statements : Rules (i) Hund's Rule (ii) Aufbau Principle (iii) Pauli Excl

NCERT Exemplar · Q44

Q. Match the following rules with their statements : Rules

(i) Hund's Rule

(ii) Aufbau Principle

(iii) Pauli Exclusion Principle

(iv) Heisenberg's Uncertainty Principle
Statements

(a) No two electrons in an atom can have the same set of four quantum numbers.

(b) Half-filled and completely filled orbitals have extra stablity.

(c) Pairing of electrons in the orbitals belonging to the same subshell does not take place until each orbital is singly occupied.

(d) It is impossible to determine the exact position and exact momentum of a subatomic particle simultaneously.

(e) In the ground state of atoms, orbitals are filled in the order of their increasing energies.

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Concept understanding — Energy Level Quantization

Energy Level Quantization: From Intuition to Precision

Imagine you're climbing a smooth ramp. You can stop at any height — 1 metre, 1.5 metres, 2.1 metres — anywhere you like. That's how we intuitively think about energy in everyday life: continuous, like a slide.

Now imagine a staircase. You can stand on step 1, step 2, or step 3 — but you cannot stand halfway between step 2 and step 3. There's no such place. The steps are discrete, not continuous.

Energy level quantization is the idea that in the microscopic world of atoms and molecules, energy behaves like a staircase, not a ramp. Electrons in an atom cannot have just any energy — they can only occupy specific, allowed energy levels. Everything else is forbidden.

Why does this happen? The core intuition

In the classical world, an electron orbiting a nucleus would continuously radiate energy, spiral inward, and crash — atoms would be unstable. But atoms are stable. Nature solved this problem by imposing a rule: the electron's angular momentum (and therefore its energy) can only take certain discrete values.

Think of a guitar string. It can only vibrate at specific frequencies — its fundamental and harmonics. You can't pluck it to produce a frequency halfway between two harmonics. The string's vibration is quantized by its boundaries. Similarly, an electron bound to a nucleus is confined in space, and that confinement forces its energy to be quantized.

Note

Quantization is not a mysterious extra rule — it emerges naturally whenever a wave (like an electron's matter wave) is confined. Confinement creates standing waves, and standing waves only exist at specific frequencies.

The precise statement

For a bound system (like an electron in an atom), the total energy $E$ of the system can only take certain discrete values:

E = E_1, E_2, E_3, \dots

where each $E_n$ is a specific, fixed number. The integer $n$ (1, 2, 3, …) is called the principal quantum number. The lowest energy level ( $n=1$ ) is the ground state; higher levels ( $n>1$ ) are excited states.

For the hydrogen atom, the allowed energies are given by:

E_n = -\frac{13.6 \text{ eV}}{n^2}

So:

$n=1$ : $E_1 = -13.6$ eV (ground state)
$n=2$ : $E_2 = -3.4$ eV
$n=3$ : $E_3 = -1.51$ eV
and so on, approaching 0 eV as $n \to \infty$ (the ionization limit)

Important

The negative sign means the electron is bound to the nucleus. Zero energy corresponds to the electron being free (ionized). The more negative the energy, the more tightly bound the electron.

How do we know this is real?

The most direct evidence comes from atomic spectra. When an electron jumps from a higher energy level to a lower one, it emits a photon of light with energy exactly equal to the difference:

\Delta E = E_{\text{higher}} - E_{\text{lower}} = hf

where $h$ is Planck's constant and $f$ is the frequency of the emitted light. …

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This question asks us to match fundamental rules governing electron behavior in atoms and subatomic particles with their defining statements. We will match each rule to its correct description, finding that Hund's Rule corresponds to (c), Aufbau Principle to (e), Pauli Exclusion Principle to (a), and Heisenberg's Uncertainty Principle to (d).

The behavior of electrons within an atom is governed by the principles of quantum mechanics. These principles dictate how electrons occupy available energy states, how they arrange themselves in orbitals, and even the fundamental limits of what we can know about them. The rules listed are foundational to understanding atomic structure and chemical properties.

Let's go through each rule and match it to its correct statement.

Pauli Exclusion Principle

This principle is fundamental to understanding electron configuration. It states that no two electrons in an atom can have the exact same set of all four quantum numbers: the principal quantum number ( $n$ ), the azimuthal quantum number ( $l$ ), the magnetic quantum number ( $m_l$ ), and the spin quantum number ( $m_s$ ).
- The principal quantum number ( $n$ ) defines the main energy shell.
- The azimuthal quantum number ( $l$ ) defines the subshell (s, p, d, f) and the shape of the orbital.
- The magnetic quantum number ( $m_l$ ) defines the orientation of the orbital in space.
- The spin quantum number ( $m_s$ ) describes the intrinsic angular momentum (spin) of the electron, which can be either $+1/2$ or $-1/2$ . Because of this principle, an atomic orbital can hold a maximum of two electrons, and these two electrons must have opposite spins.
No two electrons in an atom can have the same set of $(n, l, m_l, m_s)$ .

Comparing this with the given statements, statement (a) "No two electrons in an atom can have the same set of four quantum numbers" perfectly describes the Pauli Exclusion Principle.
- Match: (iii) Pauli Exclusion Principle $\rightarrow$ (a)
Aufbau Principle

The Aufbau principle (from the German word "Aufbau," meaning "building up") dictates the order in which electrons fill atomic orbitals in an atom's ground state. It states that electrons first occupy the orbitals with the lowest available energy levels before filling higher energy orbitals. This leads to the most stable electron configuration for an atom. The order of filling is generally determined by the $(n+l)$ rule, where orbitals with lower $(n+l)$ values are filled first. If two orbitals have the same $(n+l)$ value, the one with the lower $n$ value is filled first.

Comparing this with the given statements, statement (e) "In the ground state of atoms, orbitals are filled in the order of their increasing energies" accurately describes the Aufbau Principle.
- Match: (ii) Aufbau Principle $\rightarrow$ (e)
Hund's Rule

Hund's Rule of Maximum Multiplicity deals with how electrons fill degenerate orbitals (orbitals within the same subshell that have the same energy, e.g., the three $p$ orbitals or five $d$ orbitals). It states that electrons will occupy each orbital within a subshell singly with parallel spins before any orbital is doubly occupied (i.e., before pairing up). This arrangement maximizes the total spin multiplicity and leads to a more stable configuration due to reduced electron-electron repulsion and increased exchange energy.

Watch out

A common misconception is that Hund's rule explains why half-filled and fully-filled subshells are stable. While it leads to half-filled subshells, the rule itself describes the process of filling degenerate orbitals, not the reason for the stability of the resulting configurations.

Comparing this with the given statements, statement (c) "Pairing of electrons in the orbitals belonging to the same subshell does not take place until each orbital is singly occupied" is the direct definition of Hund's Rule.
- Match: (i) Hund's Rule $\rightarrow$ (c)
Heisenberg's Uncertainty Principle …

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Q.Match the following rules with their statements : Rules

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Rules

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