Strontium 90 is an element with a half life cycle of 28 days. How long would it take a sample of 448 g to decay to 7 g?
To solve, let's apply the formula of half-life which is:
`A = A_o 0.5^(t/t_(1/2))`
where `A` - amount of substance left , `A_o` - original amount of substance,
`t_(1/2) ` - half-life of the substance and `t` - elapsed time
Substitute the given values `A=7g` , `A_o = 448g` , and `t_(1/2)=28 days` to the formula.
Then, isolate t.
To do so, divide both sides by 448.
Then, take the natural logarithm of both sides of the equation.
As per property of logarithm, `ln 0.5^(t/28)` becomes `t/28 ln 0.5` .
Then, multiply both sides by 28.
`28ln(7/448) = t*ln0.5`
Then, divide both sides by ln 0.5.
Hence, it takes 168 days for the 448g Strontium-90 to decay to 7g.