Radioactive decay and half life

Radioactive decay is the spontaneous radioactive disintegration of an atomic nucleus, resulting in the release of energy. Some atoms are stable. Others are unstable and ‘decay’, emitting radiation to achieve a stable state. The emissions from an unstable atom’s nucleus, as it decays, can be in the form of alpha, beta or gamma radiation.

When an atom decays, it changes into another isotope, or form, of the same element or into a completely different element, in a process called transmutation. Different isotopes of the same element differ in the number of neutrons in their nuclei. Some elements reach stability via a series of steps through several isotopes, or ‘daughter products’.

One example is uranium-238 (U-238), which, through the process of radioactive decay, will eventually become a stable isotope of lead. However, this process takes billions of years. Along the way, as the U-238 isotope’s initial energy declines, it will transmute via a series of elements, each more stable than the last – thorium, radium, radon, polonium and bismuth – before it stabilizes as lead.

Alpha decay

In alpha decay, a positively-charged particle is emitted from the nucleus of an atom. This alpha particle consists of two protons and two neutrons (the same structure as a helium-4 nucleus). Although alpha particles are normally highly energetic, they travel only a few centimeters in air and are stopped by a sheet of paper or the outer layer of dead skin.

Beta decay

In beta decay, a particle is emitted from the nucleus of an atom. This beta particle is an electron with either negative or positive electric charge. Beta particles may travel metres in air and several millimetres into the human body. Most beta particles may be stopped by a small thickness of a light material such as aluminium or plastic.

Gamma decay

Gamma decay occurs because the nucleus of an atom is at too high an energy state. The nucleus ‘falls down’ to a lower energy state, emitting a high energy photon known as a gamma particle in the process. Gamma particles travel in a wave-like pattern at the speed of light. They can only be stopped by a dense material such as lead, steel, concrete or several metres of water.

Half Life of Radioactive Elements

The half-life of a radioactive element is the time that it takes for one half of the atoms of that substance to disintegrate into another nuclear form. The decay of an isotope can be measured by its half life. These can range from mere fractions of a second, to many billions of years.

ElementMost Stable IsotopeHalf-life of Most Stable Isotope
PoloniumPo-209102 years
AstatineAt-2108.1 hours
Radon.Rn-2223.82 days
RadiumRa-2261600 years
ThoriumTh-2297.54 x 104 years
UraniumU-2362.34 x 107 years
ProtactiniumPa- 2341.18 minutes

Example Rate of Radioactive Decay Problem

22688Ra, a common isotope of radium, has a half-life of 1620 years. Knowing this, calculate the first order rate constant for the decay of radium-226 and the fraction of a sample of this isotope remaining after 100 years.


The rate of radioactive decay is expressed by the relationship: k = 0.693/t1/2

Where k is the rate and t1/2 is the half-life.

Plugging in the half-life given in the problem: k = 0.693/1620 years = 4.28 x 10-4/year

Radioactive decay is a first order rate reaction, so the expression for the rate is:

log10 X0/X = kt/2.30

Where X0 is the quantity of radioactive substance at zero time (when the counting process starts) and X is the quantity remaining after time t. k is the first order rate constant, a characteristic of the isotope that is decaying. Plugging in the values:

log10 X0/X = (4.28 x 10-4/year)/2.30 x 100 years = 0.0186

Taking antilogs: X0/X = 1/1.044 = 0.958 = 95.8% of the isotope remains

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