Nuclear Forces

F_g G m₁ m₂ r² F_e K Q₁ Q₂ r² ATOMIC NATURE OF MATTER DOE-HDBK-1019/1-93 Atomic and Nuclear Physics NP-01 Page 8 Rev. 0 Newton stated that the gravitational force between two bodies is directly proportional to the masses of the two bodies and inversely proportional to the square of the distance between the bodies. This relationship is shown in the equation below. where: F = gravitational force (newtons) g m = mass of first body (kilograms) 1 m = mass of second body (kilograms) 2 G = gravitational constant (6.67 x 10 N-m /kg ) -11 2 2 r = distance between particles (meters) The equation illustrates that the larger the masses of the objects or the smaller the distance between the objects, the greater the gravitational force. So even though the masses of nucleons are very small, the fact that the distance between nucleons is extremely short may make the gravitational force significant. It is necessary to calculate the value for the gravitational force and compare it to the value for other forces to determine the significance of the gravitational force in the nucleus. The gravitational force between two protons that are separated by a distance of 10 meters is about 10 newtons. -20 -24 Coulomb's Law can be used to calculate the force between two protons. The electrostatic force is directly proportional to the electrical charges of the two particles and inversely proportional to the square of the distance between the particles. Coulomb's Law is stated as the following equation. where: F = electrostatic force (newtons) e K = electrostatic constant (9.0 x 10 N-m /C ) 9 2 2 Q = charge of first particle (coulombs) 1 Q = charge of second particle (coulombs) 2 r = distance between particles (meters) Using this equation, the electrostatic force between two protons that are separated by a distance of 10 meters is about 10 newtons. Comparing this result with the calculation of the -20 12 gravitational force (10 newtons) shows that the gravitational force is so small that it can be -24 neglected.