# Effective Half Life

• Astrophysics • Electricity • Electromagnetism • Energy • Fields • Force • Mechanics • Momentum • Nuclear Physics • Quantities & Units  • States of Matter • Waves • Key Experiments Effective half-life refers to the amount of time it takes for a certain radioactive substance in your body to decrease by half through natural processes. This is calculated by figuring out the biological half-life, which we'll talk about later. But, what exactly does "half-life" mean?

## What is half-life?

Atoms with unstable nuclei undergo radioactive decay by releasing alpha, beta, or gamma radiation to become stable. A radionuclide or radioisotope is a nuclide with an unstable nucleus. The timing of decay is unpredictable because it is a random process. Some radioisotopes can be found in nature, while others are made artificially in nuclear reactors.

If we have a lot of atoms, we can predict that decay will happen in the sample. We can measure the half-life of the sample by timing how long it takes for half of the atoms to decay. We can plot the time it takes for the sample to halve each time on a graph. The graph shows the number of nuclei left in the sample (N) and the number of halves (T). There are 5 half-lives in the graph, and T1/2 is the symbol for half-life.

The rate of radioactive decay has no connection to the physical state of radionuclide, its chemical composition, or external factors like temperature or pressure. The pink line in the graph below shows the amount of a radioactive sample remaining after several half-lives.

## Why is half-life important?

The half-life equation can help calculate the amount of time it takes for half of the atoms that have not yet decayed to do so. Here's the equation:

N = new amount of radioactive substance after decomposition.N0 = initial amount.t = time elapsed for decomposition.t1/2 = half-life.

When choosing radionuclides for medical imaging and therapy, their chemical, biological, and physical properties are taken into account. The radionuclides must be chemically suitable to bind with the molecules in the pharmaceutical product. They also need to be biologically acceptable so that they don't affect the body's functions while building up in the organ being studied. Finally, the radionuclide should have suitable physical properties like the type of radiation, the duration of half-life, and energy.

## Physical half-life

In medicine, the half-life of a radionuclide T1/2 is referred to as its physical half-life Tp. The half-life values for some commonly used medical radionuclides that can be used are listed in the table below.

## Biological half-life

Radiopharmaceuticals are created by combining radionuclides with chemical compounds. They are used in medical imaging and therapy as they can target specific tissues, cells, or organs in the body. As the body naturally goes through processes like respiration, urination, or defecation, the concentration of a radiopharmaceutical in the body will decrease exponentially with time. This is known as the biological half-life TB.

## Effective-half life formula

The effective half-life is the biological excretion along with the radioactive decay after a radiopharmaceutical enters a body. The effective half-life can be represented as:

TE = Effective Half-life. TB = Biological Half-life.TP = Physical Half-life.

Rearranging the above yields: When comparing the effective half-life and physical half-life, keep in mind that the effective half-life consists of both the physical half-life and the biological half-life.

### Factors affecting the half-life of radionuclides in medical uses

The effective half-life of Iodine-123 can be calculated using the formula:

Teff = (Tb x Tp) / (Tb + Tp)

Plugging in the values, we get:

Teff = (5.5 hours x 13.27 hours) / (5.5 hours + 13.27 hours)

Teff = 3.94 hours

Therefore, the effective half-life of Iodine-123 in the body is approximately 3.94 hours.

Effective Half-Life - Key takeaways A nuclide with an unstable nucleus is referred to as a radionuclide or radioisotope. We have a measure of half-life if we can get an overall estimate for the time it takes for half of the atoms in a sample to decay. The graph of half-life is an exponential decaying graph. In medicine, the half-life of a radionuclide T1/2 is referred to as its physical half-life Tp. A radiopharmaceutical’s concentration in the body naturally decreases exponentially with time, which is known as biological half-life TB. The effective half-life is the biological excretion along with the radioactive decay after a radiopharmaceutical enters a body.

## Effective Half Life

How to calculate half life?

Half-life can be calculated by using the formula N = N0(1/2)t/half-lifewhere N is the quantity remaining, N0 is the initial amount of that quantity, and t is the elapsed time.

What does half-life mean?

Half-life is the time it takes for half of the number of atoms in a sample to decay.

What is an example of half-life graph?

An exponential decay graph is an example of a half-life graph. 14-day free trial. Cancel anytime.    Join 10,000+ learners worldwide. The first 14 days are on us 96% of learners report x2 faster learning Free hands-on onboarding & support Cancel Anytime