What is the magnitude of the electrostatic force that the two protons inside the nucleus of a helium atom exert on each other? Why do atomic nuclei not simply explode?
To calculate the magnitude of the electrostatic force between two protons, we can use Coulomb's Law. Coulomb's Law states that the electrostatic force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * (q1 * q2) / r^2
Where:
F is the electrostatic force
k is the electrostatic constant (9 x 10^9 Nm^2/C^2)
q1 and q2 are the charges of the particles (in this case, the charges of two protons are both +1.6 x 10^-19 C)
r is the distance between the particles (helium nucleus is tightly packed, so it can be considered the radius of the helium nucleus, which is approximately 1.75 x 10^-15 m)
Plugging in the values:
F = (9 x 10^9 Nm^2/C^2) * (+1.6 x 10^-19 C * +1.6 x 10^-19 C) / (1.75 x 10^-15 m)^2
Calculating this equation will give us the magnitude of the electrostatic force between the two protons.
Now, moving on to the second part of your question, why atomic nuclei do not simply explode. The reason for this is because of another fundamental force called the strong nuclear force. The strong nuclear force is a powerful force that exists between protons and neutrons in an atomic nucleus. It is responsible for binding the protons and neutrons together and overcoming the repulsive force between the positively charged protons.
The strong nuclear force is extremely strong at very short distances, but it has a very short range, only acting within the nucleus of an atom. It only keeps the nucleus stable at very close distances. When the distance between particles becomes greater than the range of the strong nuclear force, the repulsive electrostatic force between the protons becomes dominant, and the nucleus becomes unstable.
In the case of helium, the strong nuclear force between the two protons is strong enough to overcome their electrostatic repulsion. However, for larger nuclei with more protons, there needs to be a greater number of neutrons to help stabilize the nucleus. This is why larger elements have a higher neutron-to-proton ratio, as it helps to balance out the electrostatic repulsion and maintain the stability of the nucleus.