The period number in the long form of the periodic table is equal to (i) magnetic quantum number of any elemen

NCERT Exemplar · Q8

Q. The period number in the long form of the periodic table is equal to

(i) magnetic quantum number of any element of the period.

(ii) atomic number of any element of the period.

(iii) maximum Principal quantum number of any element of the period.

(iv) maximum Azimuthal quantum number of any element of the period.

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Concept understanding — Aufbau Principle

The Aufbau Principle: Building Atoms from the Ground Up

Imagine you're building a house. You don't start with the roof — you lay the foundation first, then the walls, then the roof. Electrons in an atom behave the same way: they fill the lowest-energy "rooms" (orbitals) before moving to higher-energy ones. That's the core idea behind the Aufbau Principle.

The word Aufbau comes from German, meaning "building up" or "construction." It describes how electrons are added one by one to an atom as you move across the periodic table.

The Intuition: Why Lowest Energy First

An atom is most stable when its electrons are in the lowest possible energy states. Think of it like a ball rolling down a hill — it naturally settles at the bottom, not halfway up. If you try to put an electron into a high-energy orbital while a lower-energy orbital is empty, the atom would be unstable and the electron would "fall" down to the empty spot, releasing energy.

So nature follows the path of least energy: fill from the bottom up.

The Precise Statement

Aufbau Principle: In the ground state of an atom, electrons fill atomic orbitals in order of increasing orbital energy. Lower-energy orbitals are completely filled before electrons occupy higher-energy orbitals.

This is not a guess — it's a rule that emerges from quantum mechanics and is confirmed by experimental data (like atomic spectra and ionization energies).

The Order of Filling: The (n + l) Rule

But here's where it gets interesting: orbital energies don't simply increase with principal quantum number $n$ . For example, the 4s orbital ( $n=4, l=0$ ) actually has lower energy than the 3d orbital ( $n=3, l=2$ ). So electrons fill 4s before 3d.

To predict the correct order, use the (n + l) rule:

Tip

For an orbital with quantum numbers $n$ and $l$ , its energy increases with $(n + l)$ . If two orbitals have the same $(n + l)$ value, the one with lower $n$ fills first.

Let's check:

4s: $n + l = 4 + 0 = 4$
3d: $n + l = 3 + 2 = 5$

Since $4 < 5$ , 4s fills first. That's why potassium (atomic number 19) has the electron configuration $[\text{Ar}]\,4s^1$ , not $[\text{Ar}]\,3d^1$ .

The Complete Filling Order (Memory Aid)

Here's the sequence you'll use for most elements up to atomic number 118:

1s \rightarrow 2s \rightarrow 2p \rightarrow 3s \rightarrow 3p \rightarrow 4s \rightarrow 3d \rightarrow 4p \rightarrow 5s \rightarrow 4d \rightarrow 5p \rightarrow 6s \rightarrow 4f \rightarrow 5d \rightarrow 6p \rightarrow 7s \rightarrow 5f \rightarrow 6d \rightarrow 7p

A common trick is to write the orbitals in rows by $n$ and draw diagonal arrows:

1s
2s  2p
3s  3p  3d
4s  4p  4d  4f
5s  5p  5d  5f
6s  6p  6d
7s  7p

Follow the diagonals from top-right to bottom-left — that gives you the filling order.

Important Exceptions (Don't Panic)

The Aufbau principle works beautifully for most elements, but there are a few well-known exceptions where a half-filled or fully-filled subshell provides extra stability:

Chromium ( $Z=24$ ): Expected $[\text{Ar}]\,4s^2 3d^4$ , but actual is $[\text{Ar}]\,4s^1 3d^5$ (half-filled d-subshell is more stable) …

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The period number tells you how many electron shells are occupied; it matches the highest principal quantum number ( $n$ ) found in any element of that period. The answer is (C).

The periodic table's long form arranges elements by their electronic configuration, and the period number carries a precise quantum-mechanical meaning. To see which quantum number it corresponds to, we need to recall what each quantum number describes.

The principal quantum number $n$ specifies the shell or energy level: $n = 1, 2, 3, \ldots$ correspond to the K, L, M, … shells. The azimuthal (or angular momentum) quantum number $\ell$ describes the subshell shape within a given shell: $\ell = 0, 1, 2, 3$ correspond to s, p, d, f orbitals, with $\ell$ ranging from $0$ to $n - 1$ . The magnetic quantum number $m_\ell$ distinguishes orbitals within a subshell and ranges from $-\ell$ to $+\ell$ .

When we fill electrons according to the Aufbau principle, we add them to the lowest-energy orbitals available. The period number is defined as the number of the outermost shell that contains (or will contain) electrons as we move across that row.

Let's check each option against a few periods:

Period 1 (H, He): Electrons fill the 1s orbital. The maximum $n = 1$ , maximum $\ell = 0$ . Period number is 1.
Period 2 (Li through Ne): Electrons occupy the 2s and 2p orbitals. The maximum $n = 2$ , maximum $\ell = 1$ (for p). Period number is 2.
Period 3 (Na through Ar): Electrons fill 3s and 3p. Maximum $n = 3$ , maximum $\ell = 1$ . Period number is 3.
Period 4 (K through Kr): The filling order is 4s, then 3d, then 4p. Even though 3d is being filled, the outermost shell is the fourth ( $n = 4$ ), because 4s and 4p belong to it. Maximum $n = 4$ , but maximum $\ell = 2$ (for d). Period number is 4.
Period 6 (Cs through Rn): Includes 6s, 4f, 5d, and 6p. Maximum $n = 6$ , maximum $\ell = 3$ (for f). Period number is 6.

Now evaluate the options:

(A) Magnetic quantum number: $m_\ell$ varies within each subshell and has no systematic relationship to the period number. …

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Q.The period number in the long form of the periodic table is equal to

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