Problem 53 - A Complete Resource Book in Chemistry for JEE Main

Question

The binding energy of an element is \(64 \mathrm{meV}\). If \(\mathrm{BE} /\) Nucleon is \(6.4\), the number of nucleons are (a) 10 (b) 64 (c) 16 (d) \(6.4\)

Step-by-Step Solution

Answer

The number of nucleons is 10, option (a).

Step 1: Understanding the Formula

The binding energy per nucleon is calculated using the formula \( \text{BE per nucleon} = \frac{\text{Total Binding Energy}}{\text{Number of Nucleons}} \). We are given \( \text{BE per nucleon} = 6.4 \) meV and \( \text{Total Binding Energy} = 64 \) meV.

Step 2: Setting Up the Equation

Since we have \( \text{BE per nucleon} = \frac{64}{\text{Number of Nucleons}} = 6.4 \), we can set up the equation as \( 64 = 6.4 \times \text{Number of Nucleons} \).

Step 3: Solving for Number of Nucleons

Rearrange the equation to solve for the number of nucleons: \( \text{Number of Nucleons} = \frac{64}{6.4} \).

Step 4: Calculation

Calculate \( \frac{64}{6.4} = 10 \). So, the number of nucleons is 10.

Key Concepts

Nucleons

Nucleons are the particles that reside in the nucleus of an atom. They include two types of subatomic particles: protons and neutrons. Together, these particles make up almost the entire mass of an atom since they are much heavier than electrons, which orbit the nucleus.

• Protons: These are positively charged particles. The number of protons in the nucleus of an atom determines the chemical element.
• Neutrons: These particles have no charge (they are neutral). They play a crucial role in stabilizing the nucleus.

Understanding nucleons helps in studying the atomic structure and nuclear reactions. The total number of nucleons in a nucleus is called the "mass number". In nuclear physics, the properties and interactions of nucleons are key concepts that help explain the nature of nuclear forces and reactions.

Binding Energy per Nucleon

Binding energy per nucleon is a vital concept in understanding nuclear stability and interactions. It essentially measures how strongly each nucleon is bound within the nucleus.

• It is calculated by dividing the total binding energy of the nucleus by the number of nucleons it contains.
• A higher binding energy per nucleon indicates a more tightly bound and stable nucleus.

For example, in the given exercise, the binding energy per nucleon is 6.4 meV. This means, on average, each nucleon in the nucleus contributes 6.4 meV to the total binding energy. The stability of an atom or atomic nucleus often depends on this value. Typically, elements like iron have one of the highest binding energies per nucleon, contributing to their significant stability compared to other elements.

Nuclear Physics

Nuclear physics is the branch of science that deals with understanding the constituents and interactions of atomic nuclei. It covers a wide range of phenomena including radioactive decay, nuclear fusion, and nuclear fission.

• Radioactive decay: This is a process where unstable nuclei release energy by emitting radiation, transforming into a more stable form.
• Nuclear fission: The splitting of a heavy nucleus into smaller ones, releasing energy in the process. It is the principle behind nuclear reactors.
• Nuclear fusion: The merging of light nuclei to form a heavier nucleus, also releasing energy. This is the process powering the sun.

Nuclear physics not only helps in understanding natural phenomena but also has practical applications, including medical imaging, energy production, and developing new technologies. The field continually strives to unlock more secrets of the nucleus to advance both scientific knowledge and real-world applications.