We can think of the nucleus of an atom as a sort of drop—a bunch of
NEUTRONS and PROTONS held together by very strong short-range forces.
These elementary particles within a nucleus are not arranged in any
fixed or rigid array, but are free to move about within the grip of
these forces. These motions may be quite violent, but for most NUCLIDES
found in nature, the nuclear forces are powerful enough to keep
everything confined; thus the nuclei of these atoms hold together, and
are said to be stable. If any one nucleus of a given ISOTOPE is stable,
then all others are also stable, because what is true for one atom of a
given kind is true for all others of the same kind.[5]
Some nuclides, both man-made and natural, are unstable, however. Their
nuclei are in such violent turmoil that the nuclear forces cannot always
hold them together, and various bits and pieces fly off. If we were to
try to predict when one particular unstable nucleus would thus
disintegrate, however, we could not succeed, because the instant any
specific decay (or disintegration) event will occur is a matter of
chance. Only if a large number of unstable nuclei of one kind are
collected together can we say with certainty that, out of that number, a
certain proportion will decay in a given time. It turns out that this
proportion is the same regardless of any external conditions.
This property of nuclei to decay by themselves is called radioactivity.
Radioactive nuclei decay at constant rates regardless of temperature,
pressure, chemical combination, or physical state. The process goes on
no matter what happens to the atom. In other words, the activity inside
the nucleus is in no way affected by what happens to the ELECTRONS
circling around it. (Only in very special cases can outside disturbances
affect the radioactivity of a nucleus and then only slightly. For all
practical purposes, rates of radioactive decay are constant.)
Most radioactive nuclides have rapid rates of decay (and lose their
radioactivity in a few days, or a few years, at most); most of these are
known today only because they are produced artificially. Some of them
may have been present at the time the solar system was formed, but they
have since decayed to such insignificant fractions of their original
amounts that they can no longer be detected. Only a few radioactive
nuclides decay slowly enough to have been preserved to this day, and so
are present in nature. They are listed in Table II.
Table II RADIOACTIVE NUCLIDES WITH HALF-LIVES LARGE ENOUGH TO BE STILL
PRESENT IN USEFUL AMOUNTS ON THE EARTH[6]
PARENT Element DAUGHTER HALF-LIFE (years) Type of Decay
Product
Potassium-40 Argon-40 1.3 × 10⁹ (total) ELECTRON CAPTURE
Calcium-40 BETA DECAY
Vanadium-50 Titanium-50 ~6 × 10¹⁵ (total) Electron capture
Chromium-50 Beta decay
Rubidium-87 Strontium-87 4.7 × 10¹⁰ Beta decay
Indium-115 Tin-115 5 × 10¹⁴ Beta decay
Tellurium-123 Antimony-123 1.2 × 10¹³ Electron capture
Lanthanum-138 Barium-138 1.1 × 10¹¹ (total) Electron capture
Cerium-138 Beta decay
Cerium-142 Barium-138 5 × 10¹⁵ ALPHA DECAY
Neodymium-144 Cerium-140 2.4 × 10¹⁵ Alpha decay
Samarium-147 Neodymium-143 1.06 × 10¹¹ Alpha decay
Samarium-148 Neodymium-144 1.2 × 10¹³ Alpha decay
Samarium-149 Neodymium-145 ~4 × 10¹⁴? Alpha decay
Gadolinium-152 Samarium-148 1.1 × 10¹⁴ Alpha decay
Dysprosium-156 Gadolinium-152 2 × 10¹⁴ Alpha decay
Hafnium-174 Ytterbium-170 4.3 × 10¹⁵ Alpha decay
Lutetium-176 Hafnium-176 2.2 × 10¹⁰ Beta decay
Rhenium-187 Osmium-187 4 × 10¹⁰ Beta decay
Platinum-190 Osmium-186 7 × 10¹¹ Alpha decay
Lead-204 Mercury-200 1.4 × 10¹⁷ Alpha decay
Thorium-232 Lead-208 1.41 × 10¹⁰ 6 Alpha + 4
beta[7]
Uranium-235 Lead-207 7.13 × 10⁸ 7 Alpha + 4 beta
Uranium-238 Lead-206 4.51 × 10⁸ 8 Alpha + 6 beta
In a large number of radioactive nuclei of a given kind, a certain
fraction will decay in a specific length of time. Let’s take this
fraction as one-half and measure the time it takes for half the nuclei
to decay. This time it is called the HALF-LIFE of that particular
nucleus and there are various accurate physical ways of measuring it.
During the interval of one half-life, one-half of the nuclei will decay,
during the next half-life half of what’s left will decay, and so on. We
may tabulate it like this:
Elapsed time Amount left of
(Number of what was
half-lives) originally
present
1 ½
2 ¼
3 ⅛
4 ¹/₁₆
5 ¹/₃₂
6 ¹/₆₄
7 ¹/₁₂₈
... ...
In other words, after seven half-lives, less than 1% of the original
amount of material will still be radioactive and the remaining 99%+ of
its atoms will have been converted to atoms of another nuclide. This
kind of process can be made the basis of a clock. It works, in effect,
like the upper chamber of an hourglass. Mathematically it is written: