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) \(6.4\)

Short answer

The number of nucleons is 10.

Step-by-step solution

Identify What is Given

We are provided with the total binding energy of an element which is 64 meV, and the binding energy per nucleon is 6.4 meV.

Understanding the Relationship

The relationship between total binding energy (BE), binding energy per nucleon (BE/nucleon), and the number of nucleons (N) is given by the formula: \( \text{BE} = \text{(BE per Nucleon) } \times N \).

Set Up the Equation

Using the formula from the previous step, plug the given values into the equation: \(64 = 6.4 \times N\).

Solve for the Number of Nucleons

Rearrange the equation to solve for \(N\): \(N = \frac{64}{6.4} = 10\).

Key concepts

Binding Energy Per Nucleon

Binding energy per nucleon is a crucial concept in nuclear physics. It signifies how tightly bound the nucleons (protons and neutrons) are within a nucleus. The higher the binding energy per nucleon, the more stable the nucleus is. In our example, the binding energy per nucleon is given as 6.4 meV, which indicates the energy needed to disassemble each nucleon from the nucleus. This value is obtained by dividing the total binding energy of the nucleus by the number of nucleons present.

Understanding binding energy per nucleon can also help predict nuclear reactions and their energy outcomes.

• A high binding energy per nucleon means the nucleus is less likely to undergo fission or fusion.
• This measurement assists in identifying the most stable nuclei which often have binding energies per nucleon around 8 meV.

Nucleons Calculation

Calculating the number of nucleons in a nucleus involves the relationship between the total binding energy and the binding energy per nucleon. In the exercise, the total binding energy is provided as 64 meV, and the binding energy per nucleon is 6.4 meV. By knowing the formula \[\text{Total Binding Energy (BE)} = \text{Binding Energy per Nucleon} \times \text{Number of Nucleons (N)}\]we can rearrange this equation to solve for the number of nucleons \(N\): \[N = \frac{\text{BE}}{\text{Binding Energy per Nucleon}} = \frac{64}{6.4}=10\]

• This calculation helps us determine the structural makeup of an atom based on its nuclear properties.
• By calculating the number of nucleons, it aids in understanding the isotopic nature of elements as well.

Nuclear Physics

Nuclear physics is a branch of physics dealing with the constituents and interactions of atomic nuclei. It seeks to understand the fundamental nature of matter by exploring nuclear forces, the structure of nuclei, and nuclear reactions such as fission and fusion.
One of the primary concepts is how energy binds nucleons together within a nucleus. Scientists use nuclear physics to investigate and harness processes like:

• Radioactive decay - which involves the breakdown of an unstable nucleus into a more stable one.
• Energy production - as seen in nuclear reactors and weapons, utilizing nuclear fission.
• Medical applications - such as in imaging and cancer treatments through radiation therapy.

Overall, nuclear physics profoundly impacts technology, medicine, and our understanding of cosmic events. Its principles help clarify why certain elements undergo specific reactions and how energy is distributed among particles within a nucleus.