Test Index

Atoms and Nuclei

Section: Physics

Question : 6 of 51

Marks: +1, -0

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

E_b^p

and the binding energy of a neutron be

E_b^n

in the nucleus.

Which of the following statement(s) is(are) correct?

[JEE Adv 2022 P1]

$E_b^p-E_b^n$ is proportional to $Z(Z-1)$ where $Z$ is the atomic number of the nucleus.
$E_b^p-E_b^n$ is proportional to $A^{-\frac{1}{3}}$ where $A$ is the mass number of the nucleus.
$E_b^p-E_b^n$ is positive.
$E_b^p$ increases if the nucleus undergoes a beta decay emitting a positron.

Validate

Solution:

Binding energy of proton \& neutron due to nuclear force is same. So difference in binding energy is only due to electrostatic P.E. and it is positive

E_0^p - E_0^n =

electrostatic P.E.

= Z \times

P.E. of one proton

= Z \times \frac{1}{4 \pi \varepsilon_0} \frac{(Z-1)e^2}{R}

Where

R = R_0 A^{\frac{1}{3}}

= \frac{1}{4 \pi \varepsilon_0} \frac{Z(Z-1)e^2}{R_0 A^{\frac{1}{3}}}

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