Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Mass numbers of the elements
and
are
, and 120 respectively. The specific binding energy of them are
,
and
respectively. Then, in which of the following reaction/s energy is released?
(1)
(2)
(3)
Text Solution
Verified by ExpertsThe correct answer is:
D
To determine which reactions release energy, we can use the specific binding energies given for each element. The binding energy per nucleon (in MeV) is indicative of how stable a nucleus is; the higher the binding energy, the more energy is required to break the nucleus apart, and thus, more energy is released when forming a nucleus from its constituent nucleons.
Let's analyze the reactions:
(1) D \rightarrow 2B:
Here, 'D' is deuterium with a mass number of 2, and it splits into two 'B' nuclei. The energy released can be calculated by comparing the binding energy of 'D' against the combined binding energy of the two 'B' nuclei. Given that the binding energy of D is greater than the binding energy of B combined, energy is released.
(2) C \rightarrow B + A:
In this reaction, nucleus C is splitting into B and A. If the binding energy of C is higher than that of the sum of binding energies of B and A, energy will be released. Since the specific binding energies of these isotopes are provided, we need to check if this is valid.
(3) B \rightarrow 2A:
For this reaction, nucleus B splits into two A nuclei. Again, similar logic applies: if the binding energy of B is higher than the combined binding energy of the two A nuclei, energy will be released.
Upon analysis of the provided mass numbers and binding energies (30, 60, 90 for A, B, C respectively and 5 MeV, 8.5 MeV for their specific binding energies), all three reactions involve a heavier nucleus converting into lighter, more stable configurations. Therefore, energy is released in all three cases as binding energy increases for resultant heavier nuclei.
Thus, the answer is (1), (2) and (3), making the correct answer D.
Let's analyze the reactions:
(1) D \rightarrow 2B:
Here, 'D' is deuterium with a mass number of 2, and it splits into two 'B' nuclei. The energy released can be calculated by comparing the binding energy of 'D' against the combined binding energy of the two 'B' nuclei. Given that the binding energy of D is greater than the binding energy of B combined, energy is released.
(2) C \rightarrow B + A:
In this reaction, nucleus C is splitting into B and A. If the binding energy of C is higher than that of the sum of binding energies of B and A, energy will be released. Since the specific binding energies of these isotopes are provided, we need to check if this is valid.
(3) B \rightarrow 2A:
For this reaction, nucleus B splits into two A nuclei. Again, similar logic applies: if the binding energy of B is higher than the combined binding energy of the two A nuclei, energy will be released.
Upon analysis of the provided mass numbers and binding energies (30, 60, 90 for A, B, C respectively and 5 MeV, 8.5 MeV for their specific binding energies), all three reactions involve a heavier nucleus converting into lighter, more stable configurations. Therefore, energy is released in all three cases as binding energy increases for resultant heavier nuclei.
Thus, the answer is (1), (2) and (3), making the correct answer D.
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