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• Matter is made of molecules and atoms. Atoms consist of a nucleus (protons and neutrons) and electrons.
• Nuclear forces hold the nucleus together. Electromagnetic forces govern the interactions between electrons and the nucleus, and between electrons.
• Forces between atoms form molecules, and forces between molecules determine the structure of materials.

• The force between two atoms can be represented by a potential energy curve.
• At large separations, the potential energy decreases as the atoms get closer, indicating an attractive force.
• At a specific separation (r₀), the potential energy is minimized, the force is zero, and the atoms are in equilibrium.
• Decreasing the separation further increases the potential energy, indicating a repulsive force.
• Polyatomic molecules form when atoms arrange themselves to minimize the total potential energy.
• The force between molecules is similar: weak and attractive at large separations, increasing as separation decreases, zero at r₀, and repulsive at smaller separations.

• Atoms form molecules primarily due to electrostatic interaction between electrons and nuclei.
• These interactions are described in terms of different kinds of bonds.
• Ionic Bond: An electron is completely transferred from one atom to another, creating ions that are electrostatically attracted (e.g., Sodium Chloride).
• Covalent Bond: Described as cases when a complete transfer of electron from one atom to another does not take place.

Surface Tension: The properties of a surface are often different from the bulk properties of the material. A surface layer is approximately 10-15 molecular diameters thick because intermolecular forces become negligible beyond this distance. Origin of Surface Tension: Molecules well inside the bulk of a liquid experience equal forces from all directions. However, molecules at the surface experience asymmetric forces, primarily from the liquid below and the air above. This unbalanced force distribution leads to surface tension. Surface Tension as a Force: Imagine a line AB on the liquid surface. The surface on either side of this line pulls on the other side with a force proportional to the length of the line. These forces are perpendicular to the line and tangential to the surface. This behavior resembles a stretched rubber sheet. Definition of Surface Tension: If F is the magnitude of the force exerted on each other by two parts of the surface across a line of length l, then surface tension S is defined as S = F/l. Unit of Surface Tension: The SI unit of surface tension is N/m (Newton per meter).

• Molecules within a liquid experience balanced forces, while surface molecules experience a net inward force.
• This inward force causes microscopic turbulence at the surface, with molecules constantly being pulled back into the bulk and replaced by others.
• Work is required to move a molecule from the interior to the surface, increasing its potential energy. This extra energy is called surface energy.
• Surface tension (S) is related to surface energy.
• Consider a U-shaped frame with a sliding wire dipped in a soap solution. The soap film has two surfaces that exert a force on the wire due to surface tension.
• The force due to surface tension is F = 2Sl, where l is the length of the wire and S is the surface tension.
• The work done to increase the surface area is W = Fx = 2Slx = S(2lx). This work is stored as potential energy (U).
• The increase in surface energy is U = S(2lx).
• Surface tension is equal to the surface energy per unit area: S = U/A
• SI unit of surface tension can be expressed as J/m^2, which is equivalent to N/m.

• Consider a spherical drop of liquid with radius R.
• If the drop is small, gravity is negligible and the shape is spherical.

The excess pressure inside a mercury drop (or any liquid drop) is given by \(P - P_0 = \frac{2S}{R}\), where \(P\) is the pressure inside the drop, \(P_0\) is the pressure outside, \(S\) is the surface tension, and \(R\) is the radius of the drop.

A soap bubble has two surfaces (inner and outer) exposed to air. The excess pressure inside a soap bubble is given by \(P_2 - P_1 = \frac{4S}{R}\), where \(P_2\) is the pressure inside the bubble, \(P_1\) is the pressure outside, \(S\) is the surface tension, and \(R\) is the radius of the bubble.

When a liquid comes into contact with a solid surface, the liquid surface near the contact point is generally curved. The contact angle \(\theta\) is the angle between the tangent to the liquid surface and the tangent to the solid surface at the point of contact, measured within the liquid. If \(\theta < 90°\), the liquid wets the surface; if \(\theta > 90°\), the liquid does not wet the surface.