Question

A nucleus has a mass number of 56 and a binding energy per nucleon of 8.8 MeV, the total B.E is?

Hint:

Always check units. If mass defect ($\Delta m$) is given in amu, multiply by 931.5 to get total B.E. in MeV. Here, it was given directly.

Answer 1

Step 1: Understanding the Concept:
The Binding Energy (B.E.) per nucleon represents the average energy required to remove a single nucleon (proton or neutron) from a nucleus. It is a measure of nuclear stability. The total Binding Energy of a nucleus is the energy required to completely disassemble it into its constituent free nucleons.
Step 2: Key Formula or Approach:
The relationship between total Binding Energy, Binding Energy per nucleon, and Mass Number (\(A\)) is straightforward:
\[ \text{Total Binding Energy (B.E.)} = (\text{Binding Energy per nucleon}) \times (\text{Mass Number, } A) \]
Step 3: Detailed Explanation:
Given values from the problem:
Mass number (\(A\)) = 56
Binding Energy per nucleon (\(\text{B.E.}/A\)) = 8.8 MeV/nucleon
Calculate total B.E.:
\[ \text{Total B.E.} = 8.8 \text{ MeV/nucleon} \times 56 \text{ nucleons} \]
\[ \text{Total B.E.} = 8.8 \times 56 \]
Let's calculate: \(8.8 \times 56 = 8.8 \times (50 + 6) = 440 + 52.8 = 492.8\)
\[ \text{Total B.E.} = 492.8 \text{ MeV} \]
Step 4: Final Answer:
The total Binding Energy is 492.8 MeV.