# Sample of 82Br had an activity of 8.7E^4 atoms/min. Two days later, the activity had fallen to 3.6E^-4 atom/min. What is the half life of 82Br? Help solving this would be greatly appreciated

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Expert Answers

jeew-m | Certified Educator

Half life definition is given as;

'No one can say for sure when a particular nucleus will decay but one can predict how many in a given sample will decay over time. Radioactive elements have a half-life. The half life of any given element is the time that is required for one half of the sample to decay.'

For a radio active element we can write;

`A = A_0*(0.5)^(t/t_(1/2))`

Where

A = substance remaining

`A_0` = Inital amount of susbstance

t= time

`t_(1/2)` = half life of susbtance

For our question;

`A_0 ` =`8.7E^4`

A = `3.6E^-4`

t = 2

Apply these values in the equation and take ln both sides.

By solving the equation we can get `t_(1/2)` = 0.837 days

**Approximately it can be considered as 20 hours.**