Conceptual Physics

38.5 - The strong nuclear force

Atoms contain positively-charged nuclei that attract the negative electrons, and the

nuclei contain closely packed protons and neutrons. These conclusions bring up a

major question about the nucleus. Since protons are positively charged, and positive

charges repel, why do the protons in the nucleus not fly away from one another? In this

section, we will explore the nature of the force that holds nucleons together.

One good hypothesis would be that the force of gravity attracts them. This is a good

hypothesis, but incorrect: It turns out that gravity is far too weak. (For two protons, by

using Newton’s law of gravity and Coulomb’s law, you can calculate that the attractive

force of gravity is about 10^36 times weaker than the electrostatic repulsive force.)

One hypothesis down. Since gravity cannot explain the stability of the nucleus, the only

alternative is that there must be another attractive force. This fundamental force is

called the strong force.

The strong force has several important properties. It is “strong;” it manages to hold

together the protons in a nucleus despite their electrostatic repulsion. It always binds

particles together, even if their electric charges are the same, or if they are uncharged.

The strong force causes protons to attract protons, protons to attract neutrons, and

neutrons to attract other neutrons. The strong force acts only over a very short range.

For example, once two protons are separated by more than about 10í^15 m (roughly their

own diameter), there is hardly any attraction due to the strong force, though the electrostatic repulsion is still substantial.

Although much has been learned about the properties of the strong force from experiments, there is no simple formula to relate its strength to

distance. With the electrostatic and gravitational forces, the amount of force is inversely proportional to the square of the distance between the

particles. In contrast, no simple formula can be stated for the dependence of the strong force on distance, though there are complicated

numerical approximations.

How have physicists studied the strong force? They experiment by bombarding target nuclei with high energy particles, which are influenced by

the nuclei via the strong force or the electrostatic force. These forces can change the paths of the incoming particles. By observing the

distribution of the outgoing particles, and comparing it to the predictions of theoretical models, scientists can test these models.

Strong force

Holds particles in nucleus together

Is very strong!

Always attractive, regardless of charge

Acts only over a very short range

38.6 - Nuclear properties

Are the nucleons rigid objects, or soft, compressible ones? In other words, do they

behave like hard marbles that are clumped together, or is there some flexibility to them,

like cotton balls being crammed into a bag? These questions can be answered if we

can determine how the size of the nucleus depends on the number of nucleons in the

nucleus.

It turns out that nucleons are nearly incompressible. This conclusion can be drawn by

looking at how the radius of the nucleus relates to the number of nucleons inside. The

same experiments that physicists perform to study the strong force, where they fire

particles at nuclei, have also allowed them to measure other properties of the nucleus,

such as its size.

They have determined that the radius of an atom’s nucleus is proportional to the cube

root of its mass number. As shown in Equation 1, the radius equals the cube root of the

number of neutrons and protons, multiplied by 1.2×10í^15 m.

There are some striking implications of this simple-looking formula. It holds the answer

to our question about the rigidity of nucleons, and implies other facts about the nucleus.

Consider how the radius of a sphere relates to its volume. The volume of the spherical

nucleus is equal to 4 ʌ/3 times the radius cubed. If you cube the radius, using the

equation to the right, you are cubing A1/3, which equals A. In other words, the volume is

proportional to A, the number of neutrons and protons: Each time you add a nucleon,

you are adding roughly the same amount of volume to the nucleus.

The equation also allows one to conclude that the neutrons and protons must be tightly

packed. If there were large spaces between nucleons, then as their number increased,

the volume would increase at an even faster rate; for example, the volume would more

than double when you doubled A. (If this is not obvious to you, consider the change in

the volume of adding a tenth planet beyond Pluto, versus adding another marble to a

bag of marbles. Adding another planet would increase the volume of the Solar System

by more than the volume of the planet itself; but as you add hard marbles to a cluster of

marbles, the volume of the cluster increases by about the volume of a single marble

each time.)

The equation tells scientists that the density of all nuclear material is constant. How do

we know this? Density equals mass divided by volume, and since the mass and volume

increase at the ratio of 1:1, the density does not change.

Nuclear properties

Nucleons are nearly incompressible,

tightly packed

Nuclear density is roughly the same for

all atoms

Nuclear radius increases with

mass number, A

(^702) Copyright 2007 Kinetic Books Co. Chapter 38