7. Write notes on the following:

(a) Fajan’s rule
(b) Radio carbon dating
(c) Separation of isotopes

(a) Fajan’s Rule

Fajan’s Rule helps predict the nature of ionic bonds based on the polarizing power of cations and the polarizability of anions. It was formulated by the chemist, L. Fajans, and is particularly useful in understanding the covalent character of ionic bonds. The rule considers three main factors:

1. Size of the Cation: Smaller cations have a higher charge density and are more polarizing. This means they have a greater ability to distort the electron cloud of an anion.
2. Charge on the Cation: Cations with a higher positive charge are more polarizing because they have a stronger electrostatic field that can distort the anion’s electron cloud.
3. Size of the Anion: Larger anions are more easily polarized. Their electron clouds are more diffuse, making them easier to distort by a polarizing cation.

Applications:

• Covalent Character: According to Fajan’s Rule, the greater the polarization of the anion by the cation, the greater the covalent character of the bond. This can affect properties like bond length and bond strength.
• Examples: The rule helps explain why some compounds that are typically ionic, such as aluminum chloride (AlCl₃), exhibit significant covalent character.

(b) Radio Carbon Dating

Radiocarbon Dating is a technique used to determine the age of an archaeological sample or fossil by measuring the amount of carbon-14 it contains. This method is based on the radioactive decay of carbon-14 (¹⁴C), an isotope of carbon.

Principle:

• Carbon Isotopes: Carbon exists in nature as two stable isotopes, carbon-12 (¹²C) and carbon-13 (¹³C), and one radioactive isotope, carbon-14 (¹⁴C).
• Radioactive Decay: Carbon-14 is formed in the atmosphere and is absorbed by living organisms. When an organism dies, it stops absorbing carbon-14, and the existing carbon-14 in its remains begins to decay into nitrogen-14 (¹⁴N) at a known rate (half-life of about 5,730 years).
• Measurement: By measuring the remaining amount of carbon-14 in a sample and comparing it to the initial amount, scientists can estimate the time elapsed since the organism’s death.

Applications:

• Archaeology: Dating artifacts, fossils, and remains up to about 50,000 years old.
• Geology: Understanding the age of geological samples.

Limitations:

• Age Range: Effective for dating samples up to about 50,000 years old.
• Contamination: Samples can be contaminated with modern carbon, affecting accuracy.

(c) Separation of Isotopes

Separation of Isotopes involves isolating different isotopes of an element, which have the same chemical properties but different masses. This separation is crucial for applications in nuclear energy, medicine, and research.

Methods:

1. Gaseous Diffusion:

• Principle: Isotopes of an element in the gaseous state are separated based on their slight mass differences. Heavier isotopes diffuse more slowly than lighter ones through a porous membrane.
• Application: Historically used for the separation of uranium isotopes (U-235 and U-238) in nuclear fuel production.

1. Centrifugation:

• Principle: Isotopes are separated based on their mass using high-speed centrifuges. The heavier isotopes move to the outer edge of the rotating container, while lighter isotopes remain closer to the center.
• Application: Used for the separation of uranium isotopes and other applications requiring precise separation.

1. Electromagnetic Separation:

• Principle: Isotopes are separated based on their mass-to-charge ratio using a magnetic field. The isotopes are ionized and then passed through a magnetic field, causing them to deflect by different amounts based on their mass.
• Application: Used for the separation of isotopes of elements like uranium and lithium.

1. Laser Isotope Separation:

• Principle: Uses laser light to selectively ionize specific isotopes. The ionized isotopes are then separated based on their mass.
• Application: Advanced method used for separating isotopes like uranium-235 from uranium-238.

Applications:

• Nuclear Energy: Enrichment of uranium for nuclear reactors and weapons.
• Medicine: Production of radioactive isotopes for diagnostic and therapeutic purposes.
• Research: Studies in chemistry, physics, and biology requiring precise isotopic compositions.

These methods leverage differences in mass or nuclear properties to achieve the separation of isotopes with high precision.