Problem 36 - A Complete Resource Book in Chemistry for JEE Main

Question

The binding energy of an element is \(64 \mathrm{MeV}\). If BE per nucleon is \(6.4\), the number of nucleons are (a) 10 (b) 64 (c) 16 (d) 6

Step-by-Step Solution

Answer

The number of nucleons is 10.

Step 1: Understanding the Concept

The binding energy (BE) of an element refers to the amount of energy required to disassemble the element into its individual nucleons, which are protons and neutrons. The BE per nucleon is the binding energy divided by the total number of nucleons in the nucleus. We will use this relationship to find the total number of nucleons.

Step 2: Setting up the Equation

You are given that the total binding energy of the element is 64 MeV and the binding energy per nucleon is 6.4 MeV. To find the number of nucleons (let's call this number 'N'), we use the equation: \[ BE = N imes BE_{per\, nucleon} \] where \( BE_{per\, nucleon} = 6.4 \text{ MeV} \) and \( BE = 64 \text{ MeV} \).

Step 3: Solving the Equation

Substitute the given values into the equation: \[ 64 = N imes 6.4 \] Now solve for \( N \) by dividing both sides by 6.4: \[ N = \frac{64}{6.4} \]

Step 4: Calculating the Number of Nucleons

Perform the division: \[ N = \frac{64}{6.4} = 10 \] Thus, the number of nucleons in the element is 10.

Key Concepts

Nucleons

Nucleons are the building blocks of the atomic nucleus. These include protons and neutrons.
Protons are positively charged particles, while neutrons have no charge. Despite the difference in charge, both types of particles are roughly equal in mass, and together they create the mass of an atomic nucleus.
In any given nucleus, the sum of protons and neutrons is called the mass number or nucleon number.

• This reveals the total number of nucleons in the nucleus.
• The number of protons determines the element's identity on the periodic table.
• The number of neutrons can vary within atoms of the same element, creating different isotopes.

Every nucleon plays a critical role in the stability and identity of an atom.
Understanding the concept of nucleons is essential for grasping more complex topics in nuclear physics.

Binding Energy per Nucleon

Binding energy per nucleon is a way to measure how tightly each nucleon is held within the nucleus.
It is the total binding energy of the nucleus divided by the number of nucleons.
This value is significant because it gives an insight into the stability of a nucleus. For example:

• If the binding energy per nucleon is high, it means that the nucleus is more stable.
• A lower value suggests a less stable nucleus that could be more susceptible to breaking apart.

In the exercise provided, the binding energy per nucleon is 6.4 MeV. This means that, on average, each nucleon contributes 6.4 MeV of binding energy to keep the nucleus intact.
Such calculations help physicists understand nuclear reactions and energy release phenomena.

Nuclear Physics Concepts

Nuclear physics explores the core principles governing atomic nuclei. It's a field that delves into powerful forces and energy levels unique to the subatomic realm.
Key concepts include:

• Strong Nuclear Force: This force binds nucleons together, overcoming the repulsive electrostatic forces between protons.
• Radioactivity: Certain nuclei are unstable and release energy by emitting radiation, transforming into different elements.
• Fission and Fusion: These nuclear reactions involve splitting a heavy nucleus or combining light nuclei, respectively, both releasing copious amounts of energy.

Nuclear physics is crucial for applications ranging from energy production in nuclear reactors to understanding stellar processes.
This field of study not only aids scientific exploration but also has practical benefits in medicine and energy.