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 and the binding energy of a neutron be in the nucleus.
Which of the following statement(s) is(are) correct?
is proportional to where is the atomic number of the nucleus.
is proportional to where is the mass number of the nucleus.
is positive.
increases if the nucleus undergoes a beta decay emitting a positron.
Solution:
Total binding energy (without considering repulsions),
Where, is the nuclei under consideration.
Now, considering repulsion :
Number of proton pairs
Thus repulsion energy
Where is the radius of the nucleus
there will be no repulsion term for neutrons.
Also, since
Because of repulsion among protons,
Since in decay, number of protons decrease repulsion would decrease
increases
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