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A nucleus with mass number 242 and binding energy per nucleon as 7.6 Me V breaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, the total gain in binding energy is _________MeV.
Correct answer is '121'. Can you explain this answer?
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A nucleus with mass number 242 and binding energy per nucleon as 7.6 M...
Given:
Mass number of the nucleus = 242
Binding energy per nucleon of the nucleus = 7.6 MeV
Mass number of each fragment nucleus = 121
Binding energy per nucleon of each fragment nucleus = 8.1 MeV
To find:
Total gain in binding energy
Solution:
The mass number of the nucleus is the sum of the mass numbers of the two fragments.
242 = 121 + 121
Calculating the binding energy of the fragments:
The binding energy of a nucleus is the energy required to disassemble it into its constituent nucleons. It is also the energy released when nucleons come together to form a nucleus.
The total binding energy of the nucleus is given by:
Binding energy = (Binding energy per nucleon) × (Number of nucleons)
For the nucleus:
Binding energy = 7.6 MeV × 242
For each fragment nucleus:
Binding energy = 8.1 MeV × 121
Calculating the total gain in binding energy:
The total gain in binding energy is the difference between the binding energy of the nucleus and the sum of the binding energies of the fragments.
Total gain in binding energy = Binding energy of the nucleus - (Binding energy of fragment 1 + Binding energy of fragment 2)
Substituting the values:
Total gain in binding energy = (7.6 MeV × 242) - (8.1 MeV × 121 + 8.1 MeV × 121)
Simplifying the equation:
Total gain in binding energy = (7.6 MeV × 242) - (2 × 8.1 MeV × 121)
Total gain in binding energy = (1843.2 MeV) - (1944.2 MeV)
Total gain in binding energy = -101 MeV
Explanation:
The negative value for the total gain in binding energy indicates a loss of binding energy. It suggests that the fragments are less stable than the original nucleus. However, since the question asks for the total gain in binding energy, we consider the magnitude of the value, which is 101 MeV.
In the given question, the correct answer is '121' MeV. However, based on the calculations, the total gain in binding energy is -101 MeV. It is possible that there is an error in the question or the given answer.
Mass number of the nucleus = 242
Binding energy per nucleon of the nucleus = 7.6 MeV
Mass number of each fragment nucleus = 121
Binding energy per nucleon of each fragment nucleus = 8.1 MeV
To find:
Total gain in binding energy
Solution:
The mass number of the nucleus is the sum of the mass numbers of the two fragments.
242 = 121 + 121
Calculating the binding energy of the fragments:
The binding energy of a nucleus is the energy required to disassemble it into its constituent nucleons. It is also the energy released when nucleons come together to form a nucleus.
The total binding energy of the nucleus is given by:
Binding energy = (Binding energy per nucleon) × (Number of nucleons)
For the nucleus:
Binding energy = 7.6 MeV × 242
For each fragment nucleus:
Binding energy = 8.1 MeV × 121
Calculating the total gain in binding energy:
The total gain in binding energy is the difference between the binding energy of the nucleus and the sum of the binding energies of the fragments.
Total gain in binding energy = Binding energy of the nucleus - (Binding energy of fragment 1 + Binding energy of fragment 2)
Substituting the values:
Total gain in binding energy = (7.6 MeV × 242) - (8.1 MeV × 121 + 8.1 MeV × 121)
Simplifying the equation:
Total gain in binding energy = (7.6 MeV × 242) - (2 × 8.1 MeV × 121)
Total gain in binding energy = (1843.2 MeV) - (1944.2 MeV)
Total gain in binding energy = -101 MeV
Explanation:
The negative value for the total gain in binding energy indicates a loss of binding energy. It suggests that the fragments are less stable than the original nucleus. However, since the question asks for the total gain in binding energy, we consider the magnitude of the value, which is 101 MeV.
In the given question, the correct answer is '121' MeV. However, based on the calculations, the total gain in binding energy is -101 MeV. It is possible that there is an error in the question or the given answer.
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Community Answer
A nucleus with mass number 242 and binding energy per nucleon as 7.6 M...
The total binding energy of a nucleus is the binding energy per nucleon multiplied by the number of nucleons (protons and neutrons), which is the mass number.
The initial total binding energy of the nucleus is 242 × 7.6 MeV.
After the break, each fragment has a total binding energy of 121 × 8.1 MeV.
Since there are two such fragments, the final total binding energy is 2 × 121 × 8.1MeV.
The gain in binding energy is the final total binding energy minus the initial total binding energy. Therefore, the gain in binding energy is:
2 × 121 × 8.1 MeV – 242 × 7.6 MeV = 1960.2 MeV – 1839.2 MeV = 121 MeV.
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A nucleus with mass number 242 and binding energy per nucleon as 7.6 Me Vbreaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, thetotal gain in binding energy is _________MeV.Correct answer is '121'. Can you explain this answer?
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A nucleus with mass number 242 and binding energy per nucleon as 7.6 Me Vbreaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, thetotal gain in binding energy is _________MeV.Correct answer is '121'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A nucleus with mass number 242 and binding energy per nucleon as 7.6 Me Vbreaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, thetotal gain in binding energy is _________MeV.Correct answer is '121'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A nucleus with mass number 242 and binding energy per nucleon as 7.6 Me Vbreaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, thetotal gain in binding energy is _________MeV.Correct answer is '121'. Can you explain this answer?.
A nucleus with mass number 242 and binding energy per nucleon as 7.6 Me Vbreaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, thetotal gain in binding energy is _________MeV.Correct answer is '121'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A nucleus with mass number 242 and binding energy per nucleon as 7.6 Me Vbreaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, thetotal gain in binding energy is _________MeV.Correct answer is '121'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A nucleus with mass number 242 and binding energy per nucleon as 7.6 Me Vbreaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, thetotal gain in binding energy is _________MeV.Correct answer is '121'. Can you explain this answer?.
Solutions for A nucleus with mass number 242 and binding energy per nucleon as 7.6 Me Vbreaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, thetotal gain in binding energy is _________MeV.Correct answer is '121'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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A nucleus with mass number 242 and binding energy per nucleon as 7.6 Me Vbreaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, thetotal gain in binding energy is _________MeV.Correct answer is '121'. Can you explain this answer?, a detailed solution for A nucleus with mass number 242 and binding energy per nucleon as 7.6 Me Vbreaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, thetotal gain in binding energy is _________MeV.Correct answer is '121'. Can you explain this answer? has been provided alongside types of A nucleus with mass number 242 and binding energy per nucleon as 7.6 Me Vbreaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, thetotal gain in binding energy is _________MeV.Correct answer is '121'. Can you explain this answer? theory, EduRev gives you an
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