Enter the initial quantity, final quantity, and total time passed to calculate the half-life. Half-life is defined as the time it takes for a value to decrease by half. This is most often used in nuclear physics.

Half-Life Formula

So, how do you calculate half-life? Half-life is calculated using the exponential decay formulas, as shown below.

{displaystyle {begin{aligned}N(t)&=N_{0}left({frac {1}{2}}right)^{frac {t}{t_{1/2}}}\N(t)&=N_{0}e^{-{frac {t}{tau }}}\N(t)&=N_{0}e^{-lambda t}end{aligned}}}

Where N0 is the initial quantity
N(t) is the quantity remaining after some time
t1/2 is the half-life, and t is time.

This can be further simplified into the following to calculate half-life.

{displaystyle t_{1/2}={frac {ln(2)}{lambda }}=tau ln(2)}

What is half-life?

A half-life is the time it takes a given substance to deteriorate or lose half of its mass.

Half-life is a term mostly used in nuclear physics to describe the rate of decay of radioactive substances. As a result, the formula above includes the decay constant of the material. However, the half-life can also be calculated simply through time passed, initial quantity, and final quantity by re-arranging the very first equation above.

The idea of half-life is that since it’s exponential decay, it starts off losing a lot of mass to start, then slowly slows down. It will never actually reach absolute 0. Yet, of course, it would eventually approach an amount considered negligible.

How to calculate a half-life?

First, you must determine the initial quantity of your substance
For this example we will assume that to be 10 grams.
Next, you need to measure the time that has passed.
For this example we will assume 10 seconds.
Next, you need to measure the final quantity of substance
For this example we will assume 9 grams.
Finally, plug the needed information into the formula
79.84 is the half life.

FAQ

What factors affect the half-life of a substance?

The half-life of a substance is primarily determined by its decay constant, which is a characteristic of each radioactive material. Environmental factors typically do not affect the half-life of a substance.

Can the half-life concept apply to non-radioactive decay processes?

Yes, the concept of half-life can also apply to any process that follows an exponential decay pattern, such as the degradation of pharmaceuticals or the decay of stable isotopes in geochemistry.

How does the half-life relate to the safety of radioactive materials?

The half-life of a radioactive material is a key factor in determining its safety and handling. Materials with short half-lives decay rapidly, potentially emitting dangerous levels of radiation initially, but become safer over a short period. Conversely, materials with long half-lives emit radiation over longer periods, posing long-term hazards.

Is it possible to alter the half-life of a radioactive substance?

In general, the half-life of a radioactive substance is a fixed property and cannot be altered by physical or chemical means. However, certain nuclear reactions, such as neutron capture, can transform a nucleus into a different isotope, effectively changing its half-life.

Half Life Calculator