The Half-Life calculator can be used to understand the radioactive decay principles. It can be used to calculate the half-life of a radioactive element, the time elapsed, initial quantity, and remaining quantity of an element. Half-life is a concept widely used in chemistry, physics, biology, and pharmacology.
What is half life?
There are stable and unstable nuclei in each radioactive element. Unstable nuclei are radioactive decay and emit alpha, beta, or gamma-rays that eventually decay to stable nuclei while stable nuclei of a radioactive don’t change. Half-life is defined as the time needed to undergo its decay process for half of the unstable nuclei.
Each radioactive element has a different half life decay time. The half-life of carbon-10, for example, is only 19 seconds, so it is impossible to find this isotope in nature. Uranium-233 has a half-life of about 160000 years, on the other hand. This shows the variation in the half-life of different elements.
The concept if half-life can also be used to characterize some exponential decay. For instance, the biological half-life of metabolites.
Half-life is more like a probability measure. It doesn't mean that half of the radioactive element would have decayed after the half-life is over. However, it is a highly accurate estimate when enough nuclei are available in a radioactive element.
Half life formula
By using the following decay formula, the number of unstable nuclei in a radioactive element left after t can be calculated:
\(N(t) = N_0 \times 0.5^{(t/T)}\)
In this equation:
N(t) refers to the quantity of a radioactive element that exists after time t has elapsed.
N(0) refers to the initial amount of the element.
T refers to the half-life of an element.
The remaining amount of a material can also be calculated using a variety of other parameters:
\(N (t) = N_0 \times e^{-\dfrac{t}{\tau}}\)
\(N (t) = N_0 \times e^{(-\lambda t)}\)
λ refers to the decay constant, which is the rate of decay of an element.
τ refers to the mean lifetime of an element. The average time a nucleus has remained unchanged.
The foregoing are all three equations that characterize the radioactivity of material and are linked to each other, which can be expressed as follow:
How to calculate half life?
As of now, you have been through the formula for half-life, and you may be wondering how to find half-life by using that half-life equation. Calculating half-life is somewhat complicated, but we will simplify the process for your understanding. Let’s calculate the half-life of an element by assuming a few things for the sake of calculations.
- Suppose the original amount of a radioactive element is:
N (0) = 200 g
- Now let’s assume the final quantity of that element is:
N (t) = 50 g
- If it took 120 seconds to decay from 3 kg to 1 kg, the time elapsed would be:
t = 120 seconds
- Write the half-life equation and place the above values in that equation:
T = 60 seconds
So, if an element with the initial value of 200 grams decayed to 50 grams in 120 seconds, its half-life will 60 seconds.
Similarly, you can also calculate other parameters such as initial quantity, remaining quantity, and time by using the above equations. If you don’t want to get yourself into these complex calculations, just put the values in the above calculator. Our calculator will simplify the whole process for you.
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Example
How many grams of an isotope will remain in 30 years if the half-life of 500 grams of a radioactive isotope is 6 years?
Solution:
In this half-life problem, we already have a half-life, time, and initial quantity of a radioactive isotope. We need to calculate the remaining quantity of that isotope. Let’s find the remaining quantity step by step:
- Identify the values from the above problem description.
N (t) =?
N (0) = 500 g
T = 6 years
t = 30 years
- Write the equation of half-life and substitute the values.
- Solve the equation for the remaining quantity N (t). After simplifying these values, we will get:
N (t) = 15.625 g
A radioactive isotope will remain 15.625 grams after 30 years if its half-life is 6 years, and initial values are 500 grams. Similarly, the elapsed time t and the initial quantity N (0) of a radioactive isotope can also be calculated by following the same process.
How to use our half life calculator?
Calculating half-life using the above calculator is very simple because you just have to input values to get half-life of any element. This calculator not only calculates the half-life, but it can also be used to calculate the other parameters of the half-life equation such as time elapsed, initial and remaining value. You can find the different tabs for calculating each parameter.
To calculate the half-life of an element, go to the half-life tab:
- Enter the initial and remaining quantity of the element in the corresponding input boxes.
- Enter the total time it took to decay. You can select the unit of time from seconds, minutes, hours, months, year, etc.
- Press the Calculate It will instantly show you the half-life of the element.
Similarly, you can calculate initial and remaining values as well as the time elapsed by clicking on the respective tabs and entering values in the input boxes. You don’t need to put any effort into calculating half life because this calculator does all the complex calculations by only taking values and give the results in a blink of an eye. Moreover, you can use this calculator to solve any type of half-life problems in school or college.