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The half-life calculator is a tool that helps you understand the principles of radioactive decay. You can use it to not only learn how to calculate half-life, but also as a way of finding the initial and final quantity of a substance or its decay constant. This article will also present you with the half-life definition and the most common half-life formula.
Each radioactive material contains stable and unstable nuclei. Stable nuclei don't change, but unstable nuclei undergo a type of radioactive decay, emitting alpha particles, beta particles, or gamma rays and eventually decaying into stable nuclei. Half-life is defined as the time required for half of the unstable nuclei to undergo their decay process.
Each substance has a different half-life. For example, carbon-10 has a half-life of only 19 seconds, making it impossible for this isotope to be encountered in nature. Uranium-233, on the other hand, has a half-life of about 160 000 years.
This term can also be used more generally to describe any kind of exponential decay - for example, the biological half-life of metabolites.
Half-life is a probabilistic measure - it doesn't mean that exactly half of the substance will have decayed after the time of the half-life has elapsed. Nevertheless, it is an approximation that gets very accurate when a sufficient number of nuclei are present.
🙋 One of the applications of knowing half-life is radiocarbon dating. Learn more about that by checking out our Radiocarbon dating calculator.
We can determine the number of unstable nuclei remaining after time t t t using this equation:
N ( t ) = N ( 0 ) × 0. 5 ( t / T ) , N(t) = N(0)\times0.5^<(t/T)>, N ( t ) = N ( 0 ) × 0. 5 ( t / T ) ,It is also possible to determine the remaining quantity of a substance using a few other parameters:
N ( t ) = N ( 0 ) × e ( − t / τ ) N ( t ) = N ( 0 ) × e ( − λ t ) , N(t) = N(0)\times e^<(-t/\tau)>\\[1.0em] N(t) = N(0)\times e^<(-\lambda t)>, N ( t ) = N ( 0 ) × e ( − t / τ ) N ( t ) = N ( 0 ) × e ( − λ t ) ,
All three of the parameters characterizing a substance's radioactivity are related in the following way:
T = ln ( 2 ) λ = ln ( 2 ) × τ T = \frac<\ln(2)> <\lambda>= \ln(2)\times \tau T = λ ln ( 2 ) = ln ( 2 ) × τConfused by exponential formulas? Try our exponent calculator.
Half-life is a similar concept to doubling time in biology. Check our generation time calculator to learn how exponential growth is both useful and a problem in laboratories! Also, we use a similar concept in pharmacology, and we call it the "drug half-life". Find out more about that in our drug half-life calculator.
Half-life is defined as the time taken by a substance to lose half of its quantity. This term should not be confused with mean lifetime, which is the average time a nucleus remains intact.
To find half-life:
The half-life of radium-218 is 25.2 x 10 -6 seconds. On the other hand, one of the most common radium isotopes is radium-226, with a half-life of 1600 years!
The half-life of carbon-14 is 5730 years. This means that after 5730 years have elapsed, half of an initial quantity of carbon-14 would have disintegrated.
The half-life of uranium-238 is 4.5 billion years. It is one of the three natural occurring uranium isotopes, along with uranium-235 (700 million years), and uranium-234 (246,000 years).
