Nuclear attraction is a force that holds together the molecules in the nucleus of an atom. Remember that there are a total of three subatomic particles in an atom: protons, neutrons, and electrons. Protons are positively charged, neutrons are neutral, and electrons are negatively charged. Of the three subatomic particles, only protons and neutrons are found inside the nucleus. Nuclear attraction must occur between a neutron and a proton. This force counteracts repulsion between protons to hold the nucleus together. Electrons are found in electron shells outside the nucleus and do not participate in nuclear attraction.

Nuclear forces occur between protons and neutrons in the nucleus of an atom. Recall that quarks are elementary particles that make up composite particles called hadrons. Protons and neutrons are types of hadrons; therefore, nuclear forces occur between two hadrons.

There are four major types of fundamental forces: gravitational force, electromagnetic force, weak force, and strong force. Gravitational force is the attractive force between two bodies, electromagnetic force is a combination of the force between charges and magnetic force, weak force is the force between a W boson and a Z boson, and strong force is the force that occurs between two quarks. Nuclear forces between protons and neutrons are an effect created by the strong force between two quarks; however, nuclear forces are not classified as a type of strong force.

Since the half-life of the sample is 3 days long, throughout the course of 9 days, the sample will undergo a half-life cycle 3 times. This means we have to half the mass of the original sample 3 times.

We originally start with 

After 3 days: 

After 6 days: 

After 9 days: 

Another way to solve these types of problems is using this formula:  where  is the number of half lives. 

thus  or  of the original sample remains. 

Therefore after 9 days, there will be  of the original sample remaining.

Alpha decay is the loss of a helium atom from the original particle.

The number of protons is reduced by two, and the nuclear mass is reduced by four.

Positron emission is when the nucleus ejects a positron, or positive equivalent of an electron. It is also known as decay.

Beta decay is when the nucleus ejects a beta particle (electron).

Alpha decay is when the nucleus ejects an alpha particle (helium nucleus).

Electron capture is when the nucleus caputres an electron from the inner most shell. This process converts a proton to a neutron.

Finally, gamma decay is when an excited nucleus emits gamma rays. Gamma rays have no mass or charge.

An emission of a positron is also known to be  decay. A positron emission can be viewed as a positron being ejected; therefore, when potassium undergoes a positron emission, the daughter nucleus will be argon (Ar) with the weight of 39.

To understand how the daughter nucleus was determined, create a positron emission reaction with potassium.

This is an example of beta decay because the atomic number increases (from 6 to 7). This means a neutron has decayed into a proton, which occurs by emitting an electron, .

First note that 15g is 1/8 of the original 120-gram mass, so all but 1/8 of these radium nuclei have decayed. By definition, ½ of the nuclei decay during one half-life. So the number of nuclei remaining after n half-lives is . In this case, three half-lives have elapsed since, . The answer is 3 * 1600 = 4800 years.

In alpha decay a helium nucleus, , is emitted. Since the total number of nucleons must be conserved, the atomic number of the parent nucleus must decrease by two, and the mass number must decrease by four. Here, the new atomic number is 90 - 2 = 88, and new mass number is 234 - 4 = 230. 

When a nucleus ejects a beta particle, the element is undergoing beta decay. The ejection of a beta particle is equivalent to the ejection of an electron. When gold ejects an electron, , the product will be .