by You may have heard about ‘Half Life,’ but very few people know much about it. It is not just a term but a crucial concept in the fields of chemistry, nuclear physics, medicine, and archaeology. Students studying the aforementioned majors must be aware of this concept and know how to calculate it. Reading this article could be highly helpful for students who find half-life calculation challenging as it outlines a step-by-step guide to help them easily calculate it.
If you are interested in learning the accurate definition of half life, the formula for its calculation, and an easy method to calculate it, then read this article until the end. Let’s delve further.
What is Half Life?
Half-life is the term that is used to describe the time required by a radioactive substance to decay to half of its original mass. Simply put, the half life is a specific time duration after which the quantity of a radioactive substance becomes half of its initial value. For instance, if you have 500 grams of a radioactive substance in the beginning, it may get reduced to 250 grams after 3 years.
So, we will consider 3 years as the half-life of that particular radioactive material. The decaying process will continue, and after another 3 years, the remaining quantity of that material will become 125 grams, and so on. While it is considered a common measure to calculate radioactive decay and loss of energy by unstable atomic nuclei that emit radiation, it is also used in carbon dating and nuclear medicine.
Here is the straightforward half life formula to calculate the average span a radioactive substance will take to reach half of its initial quantity.
t1/2 = ln(2)/𝜆
- t1/2 represents the half life in the above given formula.
- ln(2) denotes the natural algorithm of 2, which is equal to approximately 0.693.
- 𝜆 represents the decay constant of the particular substance.
Another half life equation derived from exponential decay that is used for calculation is:-
Nt=N012tt12
- N(t) is the existing quantity of a particular substance after elapsed time ’t’.
- N0 is the initial quantity of the substance.
- As mentioned earlier, ‘t’ represents the elapsed time.
- t1/2 in this equation represents half life.
How to Calculate Half Life?
Considering the complexity of the aforementioned half life formula and equation derived from exponential decay, the process of calculating half life of the given substance may sound overwhelming. However, this is where an efficient half-life calculator comes into play, making things easier. This section outlines a step-by-step guide to help students easily calculate the half life of a radioactive substance. Here are a few steps you need to follow to easily calculate the half life of any substance.
Step 1: Determine Multiple Variables
You must know a few key variables to calculate half life of a particular substance accurately. These variables are listed below.
- N0 is the initial quantity of the substance before the occurrence of any decay.
- N, on the other hand, is the remaining amount of the substance after a certain period.
- Time elapsed, which is denoted as t, should be known as well.
- Half life, which is the time taken by a substance to reduce to half of its amount, should be known as well.
It is worth mentioning that all the aforementioned key variables are independent of each other. So, if you know three, you can easily calculate the fourth one.
Step 2: Use the Half Life Formula
If the decay constant, denoted by ‘𝜆’, is known, then you can easily use the basic half life formula to figure out the half life of a particular substance. This formula is quite simple: t1/2 = ln(2)/𝜆. You can easily determine the decay constant by finding out how quickly a particular substance decays over time.
If you don’t know the decay constant, then worry not. You can think of rearranging the second formula to determine the half life by considering the experimental data. Here is how the second formula looks. It can help you determine the half life of a substance by considering its remaining amount after a certain period.
t1/2 = tlog2 (N0N)
Step 3: Use a Half Life Calculator
Manual calculation of half life can be laborious, time-consuming, and prone to errors. This is especially true when you are dealing with complex cases. Hence, using a web-based half life calculator could be the perfect way to handle complex calculations and make the process significantly easier. Performing calculations using such an online tool is quite easy. All you have to do is follow a few simple steps.
- Input the initial amount of the substance (N0). Make sure you input the initial amount in the right unit. It could be grams, the number of atoms, or any other easily measurable quantity.
- Input the amount of the substance after a certain period (N). This value is important to help you figure out how much amount of a particular substance has decayed over time.
- After that, you have to input the time elapsed (t). This is a certain amount of time during which the transformation or decay of a particular substance occurs. The elapsed time is measurable in seconds, minutes, hours, days, weeks, or any other measurable unit of time.
- Once you input all the aforementioned values, the calculator will take no time to calculate the half life and display results swiftly.
As mentioned earlier, all the key variables used in the half life equation are independent of each other. So, you can input any three of them and calculate the fourth one easily using a calculator.
Step 4: Verify the Results
This is the final step; it requires you to verify the results to ensure that the values you have obtained are accurate and that there is no error in the calculation. So, you should double-check the results by manually performing calculations. Moreover, comparing your manual calculations with the results computed by a web-based half life calculator is a great way to figure out your potential mistakes and rectify them.
Conclusion
The accurate calculation of half-life is considered a fundamental skill in various notable science fields. Failure to calculate half-life or lack of knowledge about the formula can raise questions about your ability to learn and implement a valuable concept in practical life. Hence, students studying relevant majors must know how to calculate half-life. This article explains this concept and calculation method in detail. Hopefully, you will find it helpful!
