# Half Life Calculator

Half life calculator is a free online tool to calculate the half life, decay constant,initial and final amount of the substances very easily and very fastly. To find the half life we need to provide values as inputs ie.initial quantity, final quantity and total time , then click the calculate button to know the result of half life.

### Half Life - Definition

Half-life is defined as the amount of time it takes a given quantity to decrease to half of its initial value.Each radioactive material contains a stable and an unstable nuclei. Stable nuclei don't change, but unstable nuclei undergo radioactive decay, emitting alpha particles, beta particles or gamma rays and eventually decaying into a stable nuclei. Half-life is defined as the time required for half of the unstable nuclei to undergo their decay process. Half life can also be used more generally to describe any kind of exponential decay - for example,the biological half-life of metabolites

A half-life can also be determined for non-exponential decay processes, though the half-life differs completely in the decay process. In medical terms,The half-life of a drug is the time it takes for the amount of a drug's active substance in your body to reduce by half. This depends on how the body processes and gets rid of the drug.

### Half Life Formula

The half-life formula is used to find the half-life of a substance that is decaying or reducing in quantity. The formula to calculate the half-life of a substance is **N(t) = N(0) x 0.5(t/T) N(t) = N(0) x e(-t/τ) N(t) = N(0) x e(-λt) **

- Where, N(t) is the remaining amount of a substance after time t has elapsed
- N(0) is the initial amount of the substance
- T is the half-life
- t is the full time
- τ is the mean lifetime that is the average amount of time a nucleus remains intact
- λ is the decay constant.
- relationship between half-life, the time period, t1/2, and the decay constant λ is given by t12=0.693/λ.

### Half Life Examples

**Example 1:** Find the value of the decay constant of a radioactive substance having a half-life of 0.04 seconds?

**Solution:**

Given that,

half life of the substance is = 0.04

The half life formula can be used to find the half life of the substance.

t12 = 0.693/λ

λ = 0.693/0.04 = 17.325

Therefore, the decay constant of the radioactive substance is 17.325 s-1.

**Example 2:** Calculate the half-life of a radioactive substance whose disintegration constant is 0.002 1/years?

**Solution:**

Given that,

Radioactive constant λ = 0.002 1/years

The half life formula can be used to find the half life of the substance.

t12 = 0.693/λ

Half-life t½ = 0.693/λ

= 0.693/0.002 = 346.5 years

Therefore, the radioactive substance's half-life is 346.5 years.

### FAQ’s on Half Life Calculator

**1. What is meant by Half Life? **

Half-life is nothing but the time required for a quantity to reduce to half of its initial value. It is generally used in nuclear physics to know how quickly unstable atoms will undergo radioactive decay.

**2. What is the formula of half life?**

The half life formula can be used to find the half life of the substance. t12 = 0.693/λ where λ is decay constant

**3. What is the Importance of Half Life? **

Half-life is useful for determining excretion rates as well as steady-state concentrations for any specific drug.different drugs have different half life.

**4. What is the unit for half-life?**

The units of half-life are time.The half-life is the length of time that it takes for half of an initial sample to undergo a change.