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# nucleus: The Nature of the Nucleus

### Composition

Atomic nuclei are composed of two types of particles, protons and neutrons, which are collectively known as nucleons. A proton is simply the nucleus of an ordinary hydrogen atom, the lightest atom, and has a unit positive charge. A neutron is an uncharged particle of about the same mass as the proton. The number of protons in a given nucleus is the atomic number of that nucleus and determines which chemical element the nucleus will constitute when surrounded by electrons.

The total number of protons and neutrons together in a nucleus is the atomic mass number of the nucleus. Two nuclei may have the same atomic number but different mass numbers, thus constituting different forms, or isotopes , of the same element. The mass number of a given isotope is the nearest whole number to the atomic weight of that isotope and is approximately equal to the atomic weight (in the case of carbon-12, exactly equal).

### Size and Density

The nucleus occupies only a tiny fraction of the volume of an atom (the radius of the nucleus being some 10,000 to 100,000 times smaller than the radius of the atom as a whole), but it contains almost all the mass. An idea of the extreme density of the nucleus is revealed by a simple calculation. The radius of the nucleus of hydrogen is on the order of 10 −13 cm so that its volume is on the order of 10 −39 cm 3 (cubic centimeter); its mass is about 10 −24 g (gram). Combining these to estimate the density, we have 10 −24 g/10 −39 cm 3 ≈ 10 15 g/cm 3, or about a thousand trillion times the density of matter at ordinary scales (the density of water is 1 g/cm 3).

### Mass Defect, Binding Energy, and Nuclear Reactions

When nuclear masses are measured, the mass is always found to be less than the sum of the masses of the individual nucleons bound in the nucleus. The difference between the nuclear mass and the sum of the individual masses is known as the mass defect and is due to the fact that some of the mass must be converted to energy in order to make the nucleus stable. This nuclear binding energy is related to the mass defect by the famous formula from relativity , E = mc 2, where E is energy, m is mass, and c is the speed of light. The binding energy of a nucleus increases with increasing mass number.

A more interesting property of a nucleus is the binding energy per nucleon, found by dividing the binding energy by the mass number. The average binding energy per nucleon is observed to increase rapidly with increasing mass number up to a mass number of about 60, then to decrease rather slowly with higher mass numbers. Thus, nuclei with mass numbers around 60 are the most stable, and those of very small or very large mass numbers are the least stable.

Two important phenomena result from this property of nuclei. Nuclear fission is the spontaneous splitting of a nucleus of large mass number into two nuclei of smaller mass numbers. Nuclear fusion, on the other hand, is the combining of two light nuclei to form a heavier single nucleus, again with an increase in the average binding energy per nucleon. In both cases, the change to a stable final state is accompanied by the release of a large amount of energy per unit mass of the reacting materials as compared to the energy released in chemical reactions (see nuclear energy ).