Q.Which of the following materials has a positive and small value of magnetic susceptibility? (A) Cu (B) Al (C) Bi (D) Ni

Understanding Magnetic Susceptibility

Magnetic susceptibility $\chi$ measures how much a material magnetizes in response to an external magnetic field. The sign and magnitude of $\chi$ reveal the material's magnetic character.

When we say a material has "positive and small" susceptibility, we're describing paramagnetism. Paramagnetic materials contain unpaired electrons whose magnetic moments tend to align with an external field, creating a weak attraction. The susceptibility is positive (the material magnetizes in the same direction as the field) but small in magnitude, typically $\chi \sim 10^{-5}$ to $10^{-3}$.

This contrasts sharply with diamagnetic materials ($\chi < 0$, very small) and ferromagnetic materials ($\chi \gg 1$, very large and positive).

Classifying the Given Materials

Let's examine each option by its electronic structure and magnetic behavior:

1. Copper (Cu): Electronic configuration ends in $3d^{10}4s^1$. In metallic copper, the $d$-orbitals are completely filled. The material exhibits diamagnetism with $\chi \approx -10^{-5}$. The susceptibility is negative, not positive.

2. Aluminum (Al): Electronic configuration is $[Ne]3s^2 3p^1$. The partially filled $p$-orbital means aluminum has unpaired electrons. This makes it paramagnetic with a small positive susceptibility, $\chi \approx +2.2 \times 10^{-5}$. The alignment is weak because thermal agitation constantly disrupts the ordering.

3. Bismuth (Bi): Despite having some unpaired electrons in certain configurations, bismuth is the most strongly diamagnetic of all metals, with $\chi \approx -1.7 \times 10^{-4}$. The diamagnetic contribution from its filled shells overwhelms any paramagnetic effect. …

The test: a substance is paramagnetic only if it has one or more unpaired electrons; if every electron is paired it is diamagnetic.

• (A) Aluminium: $\text{Al}$ is $1s^2\,2s^2\,2p^6\,3s^2\,3p^1$ — one unpaired $3p$ electron -> paramagnetic.
• (B) Sodium chloride: an ionic solid of $\text{Na}^+$ ($[\text{Ne}]$) and $\text{Cl}^-$ ($[\text{Ar}]$); both are closed-shell with all electrons paired -> diamagnetic. …

Why "count the unpaired electrons" is not the right test here

It is tempting to call a substance paramagnetic whenever its isolated-atom electron configuration shows an unpaired electron. That works for many ions and insulating compounds, but it is not reliable for metals — their outermost electrons are not localised on one atom at all; they delocalise into a shared conduction band. A metal's net magnetic response then comes from a competition between the weak paramagnetism of these conduction electrons (Pauli paramagnetism) and the diamagnetism of all the paired, closed-shell core electrons (core/Landau diamagnetism). For copper, the core diamagnetism wins: bulk copper metal is experimentally diamagnetic (a small, negative susceptibility), even though a lone Cu atom's configuration ($[Ar]3d^{10}4s^1$) shows one unpaired electron. This is exactly why NCERT classifies substances from an experimentally verified table rather than from raw atomic configurations.

The NCERT classification (Table 5.1)

• Diamagnetic: Bismuth, Copper, Lead, Silicon, Nitrogen (at STP), Water, Sodium Chloride.
• Paramagnetic: Aluminium, Sodium, Calcium, Oxygen (at STP), Copper Chloride.
• Ferromagnetic: Iron, Cobalt, Nickel, Gadolinium, Dysprosium.

Checking each option

• (A) Copper and Aluminium — Aluminium is genuinely paramagnetic, but Copper is diamagnetic (see above). Pair fails. …

The Core Idea: Why Materials Respond Differently to Magnetic Fields

The behaviour of a material in an external magnetic field depends entirely on its magnetic susceptibility ($\chi_m$) — a measure of how easily it becomes magnetised. Paramagnetic substances have a small positive $\chi_m$ (they are weakly attracted into the field, concentrating field lines inside). Diamagnetic substances have a small negative $\chi_m$ (they are weakly repelled, expelling field lines). Copper is a classic diamagnetic material.

The trap here is that many students remember "copper is a metal" and assume metals are paramagnetic. That's wrong — most metals, including copper, silver, gold, and bismuth, are diamagnetic. Only a few metals (like aluminium, platinum, and the transition metals iron, nickel, cobalt — but those are ferromagnetic) are paramagnetic.

Step-by-Step Reasoning

1. Identify the magnetic nature of copper.

   Copper has a completely filled 3d subshell ($3d^{10}$) and one 4s electron. There are no unpaired electrons in its atomic or metallic state. Without unpaired electrons, there can be no permanent magnetic dipole moments from electron spin. The only magnetic response comes from the orbital motion of electrons, which, according to Lenz's law, produces an induced magnetic moment that opposes the applied field. This gives copper a negative susceptibility ($\chi_m \approx -9.7 \times 10^{-6}$). It is diamagnetic.

2. What happens when a diamagnetic bar is placed in an external field?

   Because the induced magnetisation opposes the field, the net magnetic field inside the bar is slightly less than the external field. The field lines are repelled — they bend away from the bar, becoming less dense inside. This is the opposite of "concentrated inside."

3. Evaluate Assertion (A).

   "When a bar of copper is placed in an external magnetic field, the field lines get concentrated inside the bar." …

Why this question tests a key phase transition

The Curie temperature ($T_C$) is a critical point for ferromagnetic materials. Below $T_C$, the material has a permanent magnetic moment even without an external field — this is spontaneous magnetization, caused by the alignment of atomic magnetic moments due to exchange interaction. Above $T_C$, thermal energy overwhelms this cooperative alignment, and the material becomes paramagnetic: it still responds to an external field, but weakly and without any permanent magnetization.

The other options are traps. A ferromagnet does not become diamagnetic — diamagnetism is a completely different, universal but very weak effect present in all materials. A paramagnet cannot become ferromagnetic above its own Curie temperature (if it has one), and it certainly doesn't become diamagnetic.

Let’s walk through the reasoning step by step.

1. What is a ferromagnetic material?

   In a ferromagnet (like iron, nickel, cobalt), atomic magnetic moments align parallel to each other over large regions (domains) even in zero external field. This alignment is due to quantum mechanical exchange interaction, which is strong enough to overcome thermal agitation below $T_C$.

2. What happens at the Curie temperature?

   As temperature rises, thermal energy increases. At $T = T_C$, the thermal energy $k_B T$ becomes comparable to the exchange energy. The spontaneous magnetization drops to zero. Above $T_C$, the moments are randomly oriented — no long-range order remains.

3. What is the magnetic behaviour above $T_C$?

   Without an external field, the net magnetization is zero. When an external field is applied, the moments partially align with it, producing a small positive susceptibility. This is exactly paramagnetic behaviour. The susceptibility follows the Curie–Weiss law:

where $C$ is the Curie constant. This is a modified version of the Curie law for paramagnets ($\chi = C/T$), showing that the transition is continuous.

4. Why not diamagnetic? …

Part (a) — A property of a paramagnetic material

The defining property: each atom/ion of a paramagnetic material carries a permanent magnetic dipole moment arising from unpaired electron spins. Consequences that follow:

• Without a field the moments point randomly, so the bulk magnetisation is zero.
• In a field they partially align, giving a small positive susceptibility and weak attraction into stronger-field regions. …