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

Short answer

The number of nucleons is 10 (Option a).

Step-by-step solution

Understand the Given Information

The problem states that the binding energy (BE) of an element is \(64\ \text{MeV}\), and the BE per nucleon is \(6.4\). We need to determine the number of nucleons in this element.

Use the Formula for BE per Nucleon

The formula for binding energy per nucleon is:\[\text{BE per nucleon} = \frac{\text{Total BE}}{\text{Number of Nucleons}}\]We are given that the BE per nucleon is \(6.4\) and the total BE is \(64\ \text{MeV}\).

Rearrange for Number of Nucleons

Rearrange the formula to solve for the number of nucleons:\[\text{Number of Nucleons} = \frac{\text{Total BE}}{\text{BE per nucleon}} = \frac{64}{6.4}\]

Calculate the Number of Nucleons

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

Key concepts

Nucleons

Nucleons refer to the particles that reside in the nucleus of an atom. These particles include protons, which are positively charged, and neutrons, which have no charge. Together, they form the building blocks of nuclei in all elements. Understanding nucleons is crucial in the study of nuclear physics because they play a fundamental role in the stability and identity of atoms.

• Protons: These are positively charged particles found in the nucleus of an atom. The number of protons determines the chemical element and its properties.
• Neutrons: These are neutral particles that help to stabilize the nucleus. They do not affect the charge but do contribute to the mass of the atom.

The number of nucleons in an atom is referred to as the mass number, which is the sum of protons and neutrons.
This concept is vital when calculating properties like binding energy, which involves the energy required to hold the nucleons together within the nucleus.

Binding Energy Per Nucleon

Binding energy per nucleon is an important concept in nuclear physics, as it helps in understanding how tightly nucleons are bound within a nucleus. When nucleons are bound together to form an atomic nucleus, energy is released, and this binding energy can be quantified per nucleon.

• Formula: The formula for calculating the binding energy per nucleon is given by \(\text{BE per nucleon} = \frac{\text{Total BE}}{\text{Number of Nucleons}}\).
• Significance: A higher binding energy per nucleon usually indicates a more stable and tightly-bound nucleus. This is crucial for understanding nuclear reactions and decay processes.

By calculating this value, scientists can gauge the stability of an element, predict nuclear fission or fusion reactions, and better understand the forces at work in atomic nuclei. For example, in the exercise provided, dividing the total binding energy by the binding energy per nucleon helps us find the total number of nucleons.

Nuclear Physics

Nuclear physics explores the components and forces at play within an atomic nucleus. It delves into understanding phenomena such as nuclear reactions, energy production, and the fundamental nature of matter.
Attempts to harness nuclear reactions for energy have revolutionized fields such as power generation and provided insights into the universe's age and processes.
Here are some key areas of study within nuclear physics:

• Nuclear Reactions: These involve changes in an atom's nucleus and can include processes like fission, fusion, and radioactive decay.
• Energy Production: Nuclear physics underpins the operation of nuclear power plants and the principles of nuclear fusion, which scientists aim to control for limitless clean energy.
• Fundamental Forces: It examines the strong nuclear force that holds nucleons together and the weak force involved in radioactive decay.

Through nuclear physics, we gain insights not just into energy and its potential uses, but also into fundamental questions about the nature of matter and the workings of the universe.