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Atoms and Nuclei question

2022 · Shift 1 · Q50
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Atoms and Nuclei question

2022 · Shift 1 · Q50

JEE AdvancedPhysicsAtoms and NucleiMultiple correct+4 / −2
The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be EbpE_{b}^{p}Ebp​ and the binding energy of a neutron be EbnE_{b}^{n}Ebn​ in the nucleus. Which of the following statement(s) is(are) correct?
  1. A
    Ebp−EbnE_{b}^{p}-E_{b}^{n}Ebp​−Ebn​ is proportional to Z(Z−1)Z(Z-1)Z(Z−1) where ZZZ is the atomic number of the nucleus.
  2. B
    Ebp−EbnE_{b}^{p}-E_{b}^{n}Ebp​−Ebn​ is proportional to A−13A^{-\frac{1}{3}}A−31​ where AAA is the mass number of the nucleus.
  3. C
    Ebp−EbnE_{b}^{p}-E_{b}^{n}Ebp​−Ebn​ is positive.
  4. D
    EbpE_{b}^{p}Ebp​ increases if the nucleus undergoes a beta decay emitting a positron.
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