What is Half Life and How to Calculate it?

Half Life Formula

We all have heard about the term Half-Life. But how many of us know its exact meaning and the ways to calculate it? You might think that what is the need of calculating half-life? But, Half-Life has paramount significance in nuclear physics. You wouldn’t have understood the concepts of unstable atom movement, radioactive decaying, atom stability, etc. without understanding half life formula and how to calculate it.

Definition of Half Life

Half-Life is the amount of time required for any given substance to reach to the half of its initial value. As stated above, it is more often used in nuclear physics and for any non-exponential or exponential decaying.

A renowned scientist named Ernest Rutherford coined this famous term in 1907 while he used the half-life formula to determine the age of the rocks by measuring the decaying period of radium to lead.

Did you know a fun fact that half-life remains constant over the whole lifetime of an exponentially decaying quantity? No? A half-life is a specific unit for exponential decay equations.

As half-life describes an exponential decaying process, it is because of this that it is utilised for defining the decay of discrete entities, including the radioactive isotopes in terms of probability. Therefore, on average, the half-life is the period required for half of all entities to decay.

Importance of Half Life

1. It enables us to discover the age of the artefacts
2. It allows us to calculate the safety period for the storage of radioactive waste until
3. Also, it allows doctors to use radioactive tracers safely
4. It also allows determining the age of any rock by its exponential decay

How to Calculate Half Life?

Now when we know what half-life is, let’s try calculating half life formula using the below listed following steps:

Step1: Exponential decay is a general exponential function of x. As x increases, f(x) decreases and approaches zero.  f(x) = a^x, where |a| < 1

Step 2: Rewrite the function in terms of half-life, which means, replace x with t. f(t) = (1/2)^t/t_1/2

Step 3: Define the initial and the final quantity, i.e., Initial Quantity: N₀(t), Final Quantity: N(t). Therefore, N(t) = N₀(1/2)^t/t_1/2

Step 4: Solve the equation to obtain half-life

• Divide both sides by the initial amount (N₀): N_t/N₀ = (1/2)^t/t_1/2
• Take the logarithm, base 1/2 of both sides log_1/2(N_t/N₀) = t/t_1/2
• Multiply both sides by t_1/2 and divide both sides by the entire left side: t_1/2= t/ log_1/2(N_t/N₀)

Therefore, the half life formula that describes all the exponential decays is:

t_1/2= t/ log_1/2(N_t/N₀)

Conclusion

Now when we have learned everything about half-life, it shows that half-life has great significance in everyday life also. It portrays us that like every other thing in this world decays, we humans tend to have the same property. If we spend time exploring something that changes now and then, we might end up wasting our time. Therefore, we need to maintain the pace to keep up with where we are, and that is what half-life portrays.

Solved Question for You

Question: What is the Half life process?

1. The time it takes for half an atom to decay.
2. There is no Half life process.
3. Process of emitting energy in the form of waves or particles.
4. Time that it takes for half the atoms of a radioactive substance to decay.

Answer: D. Half life process is defined as the time it takes for half the atoms of a radioactive substance to decay.