Paramagnetism — Revision Notes

⚡ 30-Second Revision

Definition: — Weakly attracted to external magnetic field, temporary magnetization.
Origin: — Unpaired electrons $implies$ permanent atomic magnetic moments.
Absence of Field: — Moments randomly oriented due to thermal agitation (net $M=0$).
Presence of Field: — Moments partially align with field (net $M > 0$).
Magnetic Susceptibility ($chi_m$): — Small, positive ($10^{-3}$ to $10^{-5}$).
Relative Permeability ($mu_r$): — Slightly greater than 1 ($mu_r = 1 + chi_m$).
Curie's Law: — $chi_m = C/T$ (Inverse proportionality with absolute temperature $T$).
Temperature Effect: — $chi_m$ decreases as $T$ increases.
Field Lines: — Become slightly denser inside the material.
Movement in Non-uniform Field: — From weaker to stronger field regions.
Examples: — Al, Na, O$_2$, $Cu^{2+}$, $Fe^{3+}$, Pt.

2-Minute Revision

Paramagnetism describes materials that are weakly attracted to an external magnetic field. This attraction is temporary, meaning the material loses its magnetism once the external field is removed. The fundamental cause is the presence of unpaired electrons within the atoms or molecules, which give rise to permanent atomic magnetic moments.

In the absence of an external field, these moments are randomly oriented due to thermal energy, resulting in no net magnetization. When an external field is applied, these moments partially align with the field, creating a weak, induced magnetization in the same direction.

Key characteristics include a small, positive magnetic susceptibility ($chi_m$) and a relative permeability ($mu_r$) slightly greater than 1. Crucially, paramagnetic susceptibility is inversely proportional to the absolute temperature ($T$), as stated by Curie's Law ($chi_m = C/T$).

This means paramagnetism weakens as temperature rises. Examples include aluminum, oxygen, and many transition metal ions like $Fe^{3+}$ and $Cu^{2+}$.

5-Minute Revision

Paramagnetism is a magnetic phenomenon where materials exhibit a weak, temporary attraction to an external magnetic field. This behavior originates from the presence of unpaired electrons in their atomic or molecular structure.

Each unpaired electron contributes to a permanent atomic magnetic dipole moment. Without an external field, these moments are randomly oriented due to thermal agitation, leading to zero net magnetization.

When an external magnetic field ($H$) is applied, it exerts a torque on these moments, causing a partial alignment with the field. This alignment induces a net magnetization ($M$) in the material, proportional to the applied field.

However, thermal energy continuously tries to randomize these moments, preventing complete alignment and ensuring the magnetization is weak and temporary.

Quantitatively, paramagnetic materials have a small, positive magnetic susceptibility ($chi_m = M/H$), typically in the range of $10^{-3}$ to $10^{-5}$. Their relative permeability ($mu_r = 1 + chi_m$) is consequently slightly greater than 1.

A defining characteristic is their temperature dependence, governed by Curie's Law: $chi_m = C/T$, where $C$ is the Curie constant and $T$ is the absolute temperature. This inverse relationship implies that as temperature increases, thermal agitation becomes more dominant, reducing the alignment of moments and thus decreasing the magnetic susceptibility.

Conversely, cooling a paramagnetic material enhances its paramagnetic properties. Graphically, $chi_m$ versus $T$ forms a hyperbola in the first quadrant, while $chi_m$ versus $1/T$ yields a straight line through the origin.

In a non-uniform magnetic field, paramagnetic materials move from regions of weaker field to stronger field. Common examples include aluminum, platinum, oxygen gas, and many transition metal ions like $Ti^{3+}$ (with one unpaired electron) and $Fe^{3+}$ (with five unpaired electrons).

Understanding these properties is crucial for distinguishing paramagnetism from diamagnetism and ferromagnetism in NEET.

Prelims Revision Notes

Paramagnetism: NEET Quick Recall Notes

1. Definition & Basic Behavior:

Materials weakly attracted to an external magnetic field.
Induced magnetization is in the *same direction* as the applied field.
Magnetization is *temporary*; disappears when the external field is removed.

2. Origin:

Presence of unpaired electrons in atoms/ions/molecules.
Unpaired electrons lead to permanent atomic magnetic moments (like tiny bar magnets).
In absence of field: Thermal agitation causes random orientation of moments $implies$ net magnetization is zero.
In presence of field: External field partially aligns moments $implies$ net positive magnetization.

3. Key Parameters:

**Magnetic Susceptibility ($chi_m$):**

* Small and positive ($chi_m > 0$). * Typical range: $10^{-3}$ to $10^{-5}$.

**Relative Permeability ($mu_r$):**

* Slightly greater than 1 ($mu_r > 1$). * Formula: $mu_r = 1 + chi_m$.

4. Temperature Dependence (Curie's Law):

$chi_m$ is inversely proportional to the absolute temperature ($T$).
Formula: $chi_m = C/T$, where $C$ is the Curie constant (material-specific).
Implication: — As $T$ increases, $chi_m$ decreases (paramagnetism weakens).
Graph: $chi_m$ vs. $T$ is a hyperbola; $chi_m$ vs. $1/T$ is a straight line through the origin.

5. Behavior of Magnetic Field Lines:

Field lines become slightly denser inside the paramagnetic material.
This indicates the material slightly enhances the magnetic field within itself.

6. Movement in Non-uniform Field:

Paramagnetic materials move from weaker to stronger regions of the magnetic field.

7. Examples:

Elements: Aluminum (Al), Sodium (Na), Platinum (Pt).
Molecules: Oxygen (O$_2$) - due to two unpaired electrons in its molecular orbitals.
Ions: Many transition metal ions with incompletely filled d-orbitals, e.g., $Cu^{2+}$ ($3d^9$), $Fe^{3+}$ ($3d^5$), $Ti^{3+}$ ($3d^1$).

8. Distinguish from Diamagnetism & Ferromagnetism:

Diamagnetism: — Repelled, $chi_m < 0$, $mu_r < 1$, no unpaired electrons, temperature independent.
Ferromagnetism: — Strongly attracted, $chi_m gg 0$, $mu_r gg 1$, permanent magnetization, domains, Curie temperature ($T_C$).

Vyyuha Quick Recall

Positive Attraction, Random Atoms, Magnets Align, Gone Now, Electrons Too, Inverse Susceptibility, Much Cooler.