Nucleus $A$ having $Z=17$ and equal number of protons and neutrons has $12 MeV$ binding energy per nucleonAnother nucleus $B$ of $Z=12$ has total 26 nucleons and $18 MeV$ binding energy per nucleons The difference of binding energy of $B$ and $A$ will be ___$MeV$
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Remember that the mass number is the sum of protons and neutrons. The total binding energy is the product of the binding energy per nucleon and the mass number.
Correct Answer: 6
Approach Solution - 1
Step 1: Calculate the Mass Number of Nucleus A
Nucleus A has \(Z = 17\) (number of protons). Since it has an equal number of protons and neutrons, the number of neutrons is also 17. The mass number (\(A\)) is the sum of protons and neutrons:
\[ A = 17 + 17 = 34 \]
Step 2: Calculate the Total Binding Energy of Nucleus A
The binding energy per nucleon for nucleus A is \(1.2 \, \text{MeV}\). The total binding energy is the product of the binding energy per nucleon and the mass number:
\[ BE_A = 1.2 \times 34 = 40.8 \, \text{MeV} \]
Step 3: Calculate the Total Binding Energy of Nucleus B
Nucleus B has 26 nucleons, and the binding energy per nucleon is \(1.8 \, \text{MeV}\):
\[ BE_B = 1.8 \times 26 = 46.8 \, \text{MeV} \]
Step 4: Calculate the Difference in Binding Energies
The difference in binding energies is:
\[ \Delta BE = BE_B - BE_A = 46.8 - 40.8 = 6 \, \text{MeV} \]
Conclusion: The difference in binding energy is \(6 \, \text{MeV}\).
Approach Solution -2
For A mass number
Total binding energy
For mass number
total binding energy
Difference of
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Concepts Used:
Nuclei
In the year 1911, Rutherford discovered the atomic nucleus along with his associates. It is already known that every atom is manufactured of positive charge and mass in the form of a nucleus that is concentrated at the center of the atom. More than 99.9% of the mass of an atom is located in the nucleus. Additionally, the size of the atom is of the order of 10-10 m and that of the nucleus is of the order of 10-15 m.
Read More: Nuclei
Following are the terms related to nucleus:
- Atomic Number
- Mass Number
- Nuclear Size
- Nuclear Density
- Atomic Mass Unit