Question

A proton and a neutron are both shot at $100{\text{m}}{{\text{s}}^{ - 1}}$ towards a $_6^{12}{\text{C}}$ nucleus. Which particle, if either, is more likely to be absorbed by the nucleus?
A) The proton
B) The neutron
C) Both particles are about equally likely to be absorbed.
D) Neither particles will be absorbed.

Answer 1

Both the proton and the neutron are shot with the same velocity towards the carbon nucleus. A nucleus consists of protons and neutrons and has a positive charge. The neutron is a chargeless particle and so will not contribute to the charge of the nucleus. So the charge of the nucleus is entirely due to the protons in it. Like charges repel.

Complete step by step answer:
Step 1: Describe the nature of the force between the carbon nucleus and the proton and the neutron.
The atomic number of the given carbon nucleus is $Z = 6$. This suggests that there are six protons in the given carbon nucleus.
The mass number of the carbon nucleus is $A = 12$. This suggests that there are six neutrons in the given carbon nucleus.
The carbon nucleus will have a charge of $+ 6e$ corresponding to the charges of the six protons in it.
As both the carbon nucleus and the incoming proton carry a positive charge, the force between the carbon nucleus and the proton will be repulsive in nature.
The neutron is chargeless and so can be absorbed by a carbon nucleus.
The given carbon nucleus $_6^{12}{\text{C}}$ is, however, a stable isotope of carbon. So neither absorption of the neutron nor the proton is likely to occur.
So the correct option is D.

Note: An unstable nucleus will absorb a neutron or a proton to become stable. A nucleus of an element is generally represented as $_Z^A{\text{X}}$ where $A$ is the mass number of the nucleus and $Z$ is the number of protons in the nucleus. The number of neutrons in the given carbon nucleus $_6^{12}{\text{C}}$ is given by, $N = A - Z = 12 - 6 = 6$. A stable nucleus is the one with proton to neutron ratio close to 1.