Question

The half life of the radioactive element Strontium-90 is 37 years. In 1950, 15 kilograms of this element released accidentally. How do you determine the formula which shows the mass remaining after t years?

Answer 1

`N(t) = 15Kgxx(1/2)^(t/color(red)37)`

Note: The half life of Strontium-90 is now published as 28.8 years. This will require adjustments of all the following values in `color(red)(red)`.

Explanation:

The formula for the half life of an exponentially decaying substance is:

`N(t)=(No)xx(1/2)^(t/(t1/2))`

`N(t)` ... is how much is still here.
`No` ... is how much we started with.
`t` ...... is the time we have measured since the start of the decay.
`t1/2` ... is the already calculated half life of the specific substance.

To calculate the mass of Strontium-90 remaining after `t` years, plug in the given values into the formula:

`N(t) = 15Kgxx(1/2)^(t/color(red)37)`

For example `color(red)37` years after 1950, the remainder of the `15Kg` of Strontium-90 released would be:

`N(67) = 15Kgxx(1/2)^color(red)(37/37) = 15Kgxx(1/2) = 7.5Kg`

In 2017 (now) the amount left is `15Kg xx (1/2)^color(red)1.8 = color(red)4.3Kg`