The half-life of Strontium-90 is 28.79 years. If a sample ends with 4.70 mg, how many mg will was at the beginning if deteriated 177.7 years? mg

Answer 1

Suppose we start with x mg

Then after t years we have x (0.5)^t/H

where H is the half-life (years)

So here we have

4.70 = x (0.5)^177.7/28.79

^{From this you can calculate x}

Answer 2

For a 1st order decay, the fraction remaining (FR) at any time is equal to 0.5ⁿ where n is the number of half lives that have elapsed. In equation form, it looks like this:

FR = 0.5ⁿ

In this problem, we have the half life of 28.79 years.

We can easily find the number of half lives that have elapsed as 177.7 yrs x 1 half life/28.79 yrs = 6.172 = n

Then FR = 0.5^6.172

FR = 0.01387 and this is equal to 4.70 mg

So, how much was there to begin with?

0.01387 x = 4. 70 mg

x = 339 mg