Half Life Calculator

Half-life is defined as the period of time that takes from a substance to undertake decay to decrease by half. This is normally used to give details of the quantities undergoing exponential decay. If we want to think of an example, it is radioactive decay.

The Half-life principle was first introduced in 1907 by the physicist Rutherford. Similar to the name, Half-life is represented as t_1/2 and it is in units of time. Basically, this Half-life is used to decide the atoms which are stable and which are unstable.

We have shared with you this tool to convert complex problems into simple problems. Here, Check out how to use this calculator step by step.

• First, read the problem to know what you need to find in the problem.
• After that, our calculator will automatically give you the suitable numbers for it.
• Just by clicking on calculate and you will get the answer in seconds.

In this, we have half-life equations that were used in the half-life calculator to calculate half-life and now we will see what those formulas or equations are.

Half-life formula,

N(t) = N(0) * 0.5^{(t/ T)}

Here, T can also be written by t^(1/2),

Where,

N(t) = Left over quantity

N(0) = Initial quantity of a substance

T = Half-life

t = Total time

In this, Half life T = 0.693 / λ

Where,

λ = decay constant

Here, we are going to see how to calculate the half-life with some solved examples. So that you can easily understand how you need to use the above formula.

Examples

Question 1: Calculate the remaining quantity, as the initial quantity is 7s and the total time is 12s and finally, the decay constant is 7s?

Solution:

Given that

Initial Quantity N(0) = 7s

Decay constant λ = 8s

Total time t = 13s

Half-life T =?

Remaining Quantity N(t) =?

Now, we will find total time T,

T = 0.693/λ = 0.693 / 7 = 0.086

Half Life, T = 0.086s

And now, we have all the values to find the remaining quantity.

Remaining Quantity N(t) = N(0) * 0.5^{(t/ T)} = 7 * (0.5 )^{13 /0.086} = 4.67 * 10 ^-45

In the same process, you can find decay constant and also initial quantity, Total time by following the above steps.

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1. Is Half-life accurate?

Yes. Half-life is accurate.

2. What is the formula for half-life?

Formula for half life, N(t) = N(0) * 0.5^{(t/ T)}

3. How long is a Half-life?

Half-life is about 12 years in length.

4. What is meant by Half-life?

Half-life is defined as the time required for a substance or quantity to reduce the initial value to half.

5. Are the numbers positive or negative in the Half-life formula?

As the half-life is shown in the form of time, it will always be in a positive number.