Physics · Ch 13 — Nuclei

Atomic Masses and Composition of Nucleus

13.2

Atomic Masses and Composition of Nucleus

13.2 Atomic Masses and Composition of Nucleus

The Need for a Special Mass Unit

The mass of a single atom is extraordinarily small when measured in kilograms. A carbon-12 atom, for instance, has a mass of only $1.992647 \times 10^{-26}$ kg. Working with such tiny numbers in kilograms is inconvenient, so physicists and chemists defined a more practical unit specifically for atomic masses.

The atomic mass unit (u) is defined as exactly one-twelfth of the mass of a carbon-12 atom. Mathematically:

1 \text{ u} = \frac{\text{mass of one }^{12}\text{C atom}}{12} = \frac{1.992647 \times 10^{-26} \text{ kg}}{12} = 1.660539 \times 10^{-27} \text{ kg}

This definition makes the mass of a carbon-12 atom exactly 12 u by construction.

Atomic Masses and the Integral Mass Rule

When atomic masses of various elements are expressed in atomic mass units, they come remarkably close to being whole-number multiples of the mass of a hydrogen atom. This pattern suggests that atoms are built from some fundamental building block of roughly unit mass.

However, there are notable exceptions. Chlorine, for example, has an atomic mass of 35.46 u — not an integer. The reason lies in the fact that most elements are mixtures of different atomic species.

Isotopes: Same Element, Different Mass

Accurate mass measurements using a mass spectrometer reveal that atoms of the same element can have different masses while exhibiting identical chemical properties. Such atomic species are called isotopes (from Greek: isos = same, topos = place — they occupy the same position in the periodic table).

Practically every element consists of a mixture of several isotopes, each with its own relative abundance.

Example: Chlorine Isotopes

Chlorine has two naturally occurring isotopes:

Isotope	Mass (u)	Relative Abundance
$^{35}\text{Cl}$	34.98	75.4%
$^{37}\text{Cl}$	36.98	24.6%

The average atomic mass of chlorine is the weighted average:

\text{Average mass} = \frac{75.4 \times 34.98 + 24.6 \times 36.98}{100} = 35.47 \text{ u}

This weighted average matches the experimentally observed atomic mass of chlorine (35.46 u), confirming the isotopic mixture.

Example: Hydrogen Isotopes

Even the lightest element, hydrogen, has three isotopes:

Isotope	Mass (u)	Relative Abundance
Protium ( $^1_1\text{H}$ )	1.0078	99.985%
Deuterium ( $^2_1\text{H}$ )	2.0141	~0.015%
Tritium ( $^3_1\text{H}$ )	3.0160	Trace (unstable)

The nucleus of the lightest hydrogen atom is called the proton. Its mass is:

m_p = 1.00727 \text{ u} = 1.67262 \times 10^{-27} \text{ kg}

This equals the mass of a hydrogen atom (1.00783 u) minus the mass of a single electron ( $m_e = 0.00055$ u).

Deuterium and tritium are the other two isotopes. Tritium nuclei are unstable and do not occur naturally — they are produced artificially in laboratories.

Charge and Composition of the Nucleus

The positive charge in the nucleus comes from protons. Each proton carries one unit of fundamental charge ( $+e$ ) and is stable.

Watch out

It was once thought that the nucleus might contain electrons, but this idea was ruled out using arguments from quantum theory. All electrons of an atom are outside the nucleus.

The number of electrons outside the nucleus equals the atomic number Z. Since the atom is electrically neutral, the total charge of the nucleus must be $+Ze$ , meaning the nucleus contains exactly Z protons.

The Discovery of the Neutron

The existence of isotopes posed a puzzle. Deuterium and tritium are isotopes of hydrogen, so each must contain exactly one proton. Yet their nuclear masses are in the ratio 1:2:3. This means deuterium and tritium nuclei must contain additional neutral matter — approximately one and two proton-mass units, respectively.

This suggested that nuclei contain neutral particles in multiples of some basic unit.

Chadwick's Experiment (1932)

James Chadwick bombarded beryllium nuclei with alpha-particles (helium nuclei) and observed the emission of neutral radiation. This radiation could knock protons out of light nuclei such as helium, carbon, and nitrogen.

The only known neutral radiation at the time was photons (electromagnetic radiation). However, applying conservation of energy and momentum showed that if the radiation were photons, their energy would need to be far higher than what the alpha-particle bombardment could provide.

Chadwick's solution: the radiation consisted of a new type of neutral particle — the neutron. From conservation of energy and momentum in the collision experiments, he determined that the neutron's mass was very nearly equal to the proton's mass.

The currently accepted mass of a neutron is:

m_n = 1.00866 \text{ u} = 1.6749 \times 10^{-27} \text{ kg}

Note

A free neutron is unstable. It decays into a proton, an electron, and an antineutrino, with a mean life of about 1000 seconds. Inside the nucleus, however, the neutron is stable.

Chadwick received the 1935 Nobel Prize in Physics for this discovery.

Describing the Nucleus: Key Quantities

The composition of any nucleus is described by three fundamental numbers:

Z = \text{atomic number} = \text{number of protons}

The term nucleon refers to either a proton or a neutron. Thus the number of nucleons in an atom is its mass number A.

Notation for Nuclides

A nuclear species (nuclide) is denoted by:

^A_Z\text{X}

where X is the chemical symbol of the element. …

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