The half-life of a substance is the time it takes for half of the atoms of that substance to decay.

Formula for half-life:

t = ln(2) / λ

where:

• t is the half-life
• ln is the natural logarithm
• λ is the decay constant

Explanation:

• The half-life is a constant for a particular substance.
• It is a measure of how quickly the substance decays.
• The half-life determines the rate of decay.
• After one half-life, half of the atoms of the substance will have decayed.
• After two half-lives, half of the remaining atoms will have decayed.
• After three half-lives, half of the remaining atoms will have decayed.

Examples:

• The half-life of carbon-14 is 5,730 years. This means that half of the carbon-14 atoms in a sample will decay to carbon-12 in 5,730 years.
• The half-life of iodine-131 is 8 days. This means that half of the iodine-131 atoms in a sample will decay to iodine-127 in 8 days.

Applications:

• Half-life is used to determine the decay constant of a substance.
• It is used to calculate the decay time of a substance.
• It is used to measure the half-lives of various substances.

Additional Notes:

• The half-life is a logarithmic quantity, meaning that it is measured in units of time that are multiples of the previous time interval.
• The half-life is a constant for a particular substance at a given temperature.
• The half-life can vary for different substances.
• The half-life is an important concept in many fields of science, including chemistry, physics, and biology.