Question

Activity 27-2. Nuclear forces and nuclear binding energy [Accompanies Section 27-2] The illustration shows two different nuclei that contain three 3H: 1 proton (p), 2 neutrons (n) nucleons. ?H (hydrogen-3) has one proton and two neutrons, n pn and He (helium-3) has two protons and one neutron. For the + purposes of this problem, treat the nucleons in each nucleus as lying along a line, as shown. 3He: 2 protons (p), 1 neutron (n) р n р (a) Rank the following forces from most attractive to most + repulsive. (Include the effects of both the strong nuclear force and the electric force.) For each force state whether the force is attractive or repulsive. If any two forces are equally attractive or equally repulsive, state this. Explain how you made your ranking (i) In PH the force of the left-hand neutron on the central proton (ii) In ’H the force of the left-hand neutron on the right-hand neutron (iii) In 'He the force of the left-hand proton on the central neutron (iv) In 'He the force of the left-hand proton on the right-hand proton - (b) Based on your results in part (a), of the two nuclei, ’H and He, which has the greater binding energy? Explain your reasoning.

Answer 1

* Proton is a positively charged, whereas neutron is neutral. Thus the force exists between two protons is the mutual force of electrostatic repulsion which does not exists between proton-neutron or neutron-neutron.

a) In  
H

i)   Between a proton and nucleon only nuclear force exists. F_pn

_ii) Between a  nucleon and nucleon only nuclear force exists. F_nn

  Hence Between a proton and other nucleon only nuclear force exists   F_pn=F_nn.

In
He

iii)   Between a proton and nucleon only nuclear force exists. F_pn

iv) Strong nuclear force exists which keeps them together inside the nucleus. As they held similar charge repel each other.This force of mutual repulsion decreases overall attraction between them.

F_pp<F_pn

Inside a nucleus  F_pp<F_pn=F_nn.

b) The binding energy of a
H
nucleus is 8.482 Mev.

The binding energy of a
He
nucleus is 7.718 Mev.

The difference between the binding energy of the two nucleus is 0.764Mev

The above difference in binding energy is due to the force of mutual repulsion between two protons in the
He
nucleus.