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In 1896 Becquerel discovered uranium radioactivity and with the Curies opened the door to the nucleus of the atom. Soon after three types of decay were established. They are $\alpha$, $\beta$ and $\gamma$ decay. Radioactive decay phenomena continue to provide us with us many important messages.

The radioactive decay is calculated by using the formula.

$A = A_{o}e^\left (\frac{-0.693t}{T{\frac{1}{2}}} \right)$

Although the radioactive decay constants are independent of temperature and pressure, the retention of the radiogenic daughter in a mineral depends strongly on temperature.

Below is given a default isotope, you can see how the half life is calculated.

## Steps for Radioactive Decay Calculator

Step 1 :

Read the problem and list the given values.

Step 2 :

Enter the isotopes in the first calculator and find out the half life value.

Step 3 :

Substitute the value of half life and the given values in the formula to find out the radioactive decay.

$A = A_{o}e^\frac{-0.693t}{T{\frac{1}{2}}}$

## Problems on Radioactive Decay Calculator

1. ### Calculate the radioactive decay for the isotope Actinium 227 whose initial activity is 4.5 and the decay time is 0.25sec?

Step 1 :

Given data

Initial activity (Ao) = 4.5

Decay time (t) = 0.25sec

Step 2 :

The half life value for the Actinium 227 isotopes is calculated as 21.77 years.

T1/2 = 21.77 years

Step 3 :

Substitute all the values in the corresponding formula.

$A = A_{o}e^\frac{-0.693t}{T{\frac{1}{2}}}$

$A = 4.5 e^\frac{-0.693(0.25)}{21.77}$

A = 4.46 years

The final activity is A = 4.46 years

2. ### Calculate the final radioactivity of Cobalt 57 isotope whose initial activity is 6.8 and the decay time is 0.86.

Step 1 :

Given data

Initial activity (Ao) = 6.8

Decay time (t) = 0.86

Step 2 :

The half life value for the Cobalt 57 isotopes is calculated as 270 days.

T1/2 = 270 days

Step 3 :

Substitute all the values in the corresponding formula.

$A = A_{o}e^\frac{-0.693t}{T{\frac{1}{2}}}$

$A = 6.8 e^\frac{-0.693(0.86)}{270}$

A = 6.78