Why Do Larger Atomic Nuclei Require More Neutrons?

[nathan17]

Radioactivity Justification

1. The problem statements, all variables and given/known data
1a. Justify the appropriate charge and mass number values for an electron, a positron, a neutrino and an antineutrino.

1b. Justify the appropriate charge and mass number values for a gamma ray.

1c. Using the properties of the attractive nuclear force and the repulsive electrostatic force between protons, discuss the reason for the increase in the neutron-to-proton ratio of stable nuclei as the atomic number increase.

Homework Equations

N.A

The Attempt at a Solution

I'm not really sure on how to go about these questions, I am currently on school holidays and the end of year exams keep getting closer and closer so I really want to try get as much work as possible done to ensure that I get a pass in my subjects.

For the first two I think that I am supposed to justify using the laws of conservation (energy, momentum, nucleons, charge (?)) but I don't know how.

For the third question, I'm not sure, but is this correct:
When the mass of the nucleus increases the number of protons increase. Due to this increase, the electrostatic repulsive force increases, this force is long ranged. The addition of neutrons provide an attractive force to increase the spacing between protons, which reduces the average repulsive force per proton

If anyone could shed some light onto this for me, I would greatly appreciate it!

I appologise if I have posted in the wrong section, but seeing how this relates somewhat to coursework (The curriculum statement questions) I figured this would be the best place.

Thankyou,
Nathan

 

[Nate810]

.Answer:1a. Electron: Charge = -1, Mass number = 0; Positron: Charge = +1, Mass number = 0; Neutrino: Charge = 0, Mass number = 0; Antineutrino: Charge = 0, Mass number = 0. These values are determined by the conservation laws of energy, momentum and charge. 1b. Gamma Ray: Charge = 0, Mass number = 0. Gamma rays have no charge and no mass, as they are composed of pure energy and are not particles. 1c. As the atomic number increases, the ratio of neutrons to protons in a nucleus must increase in order to balance the attractive nuclear force and the repulsive electrostatic force between protons. This is necessary in order to achieve a stable nucleus. The addition of neutrons provides an attractive force, which increases the spacing between protons, and thus reduces the average repulsive force per proton.

 

[baba89]

Hello Nathan,

I can understand your confusion with these questions. Let me provide some clarification and justification for the values of charge and mass number for the particles mentioned.

1a. The electron has a charge of -1 and a mass number of 0. This is because it is a fundamental particle with no substructure and a very small mass compared to that of a proton or neutron. The positron, which is the antiparticle of the electron, has the opposite charge of +1 and the same mass number of 0. This follows the law of conservation of electric charge. The neutrino and antineutrino have a charge of 0 and a mass number of 0, as they are also fundamental particles with very small masses.

1b. A gamma ray does not have a charge or a mass number, as it is a high-energy photon with no substructure. It carries energy and momentum, but not charge or mass.

1c. The increase in the neutron-to-proton ratio in stable nuclei as the atomic number increases can be explained by the balance between the attractive nuclear force and the repulsive electrostatic force. The nuclear force is strong and short-ranged, holding the nucleus together. As the number of protons increases, so does the repulsive electrostatic force between them. To counteract this repulsion and maintain stability, additional neutrons are needed to provide an attractive force and increase the spacing between protons. This results in a higher neutron-to-proton ratio in larger nuclei.

I hope this helps to clarify the concepts and provide justification for the values mentioned. Keep up the hard work in your studies!