Question

What is meant by the half-life of a radioactive isotope? How is the half-life used in radiometric age daring?

Short answer

Half-life is the time for half of a radioactive isotope to decay; it's used to calculate the age of objects by measuring remaining isotopes.

Step-by-step solution

Define Half-Life

Half-life is the time required for half of the radioactive nuclei in a sample to decay. It's a constant property unique to each radioactive isotope, representing a predictable timescale over which the isotope's radioactive atoms decrease in number.

Relate Half-Life to Radioactive Decay

During each half-life period, the quantity of the radioactive isotope reduces to half, and this process continues consistently over time. For example, if you start with 100 grams of a substance with a half-life of 1 year, only 50 grams will remain after 1 year, and 25 grams after 2 years.

Explain Radiometric Age Dating

Radiometric age dating uses the principle of half-life to estimate the age of rocks, fossils, or other objects. Scientists measure the remaining quantity of a radioactive isotope and its decay products to determine how many half-lives have passed since the object formed.

Calculate the Age Based on Half-Lives

The age of a sample can be calculated by multiplying the number of elapsed half-lives by the duration of the isotope’s half-life. This provides an estimate of the time elapsed since the radioactive isotope began to decay.

Key concepts

Half-Life

Half-life is a crucial concept in understanding radioactive substances. It refers to the amount of time it takes for half of the radioactive nuclei in a given sample to undergo decay. Each radioactive isotope has a unique half-life that does not change, no matter the amount of substance or its condition. This makes half-life a reliable measure for scientists. Knowing the half-life of a substance allows scientists to predict how fast or slow a radioactive isotope will decay over time.

• The half-life is a constant value for a specific isotope.
• Helps in predicting the behavior of radioactive substances.
• Used in various applications like radiometric age dating.

For instance, imagine a situation where you have 100 grams of a radioactive isotope with a half-life of 2 years. After 2 years, only 50 grams of the original isotope would remain, because half of the atoms have decayed. After another 2 years (making it 4 years in total), you'd be left with 25 grams, and so on. This systematic decrease helps in calculations and predictions.

Radioactive Decay

Radioactive decay is the process through which an unstable atomic nucleus loses energy by emitting radiation. This process continues until a stable state is reached. It can happen in different ways: by releasing alpha particles, beta particles, or gamma rays. The decay is spontaneous, meaning it happens naturally without any external force. As a result of decay, the element might transform into another different element.

• Natural and spontaneous process.
• Can result in the emission of alpha particles, beta particles, or gamma rays.
• Transmutations can change one element into another.

Let's say you have a radioactive isotope that undergoes beta decay. This means that during its decay, it emits a beta particle (an electron) and transforms into a different element. The speed of this decay depends on the isotope's half-life. Over time, as the isotope decays, it continues to convert to either a stable form or another element through different stages of decay.

Radioactive Isotope

A radioactive isotope, often called a radioisotope, is a version of an element that has an unstable nucleus. This instability causes the nucleus to lose energy rapidly by emitting radiation, a process known as radioactive decay. Not all isotopes are radioactive; stability varies among different isotopes of the same element.

• Atoms with an unstable nucleus that emit radiation.
• Different isotopes of an element can behave differently.
• Used in medical imaging, radiometric dating, and other scientific fields.

An isotope is defined by the number of neutrons in its nucleus. For example, Carbon-12 and Carbon-14 are isotopes of Carbon; Carbon-12 is stable, while Carbon-14 is radioactive and used in dating ancient objects. This distinctive decay property allows radioactive isotopes to serve as "clocks" in radiometric dating, enabling scientists to determine the ages of artifacts, rocks, and more by calculating how many half-lives have elapsed since formation.