Question

The quantity, q grams, of the radioactive isotope strontium-90 present in a sample decreases by half over a period of about t = 28.8 years. if a sample initially contains 3 grams of strontium-90, what equation represents the relationship between q and t?

Answer 1

notice q=3/2, is half of the original q = 3(1/2)t/28.8
your welcome

Answer 2

Step-by-step explanation:

Mass of the strontium-90 present at initial stage=
`N_o=3 grams`

Mass of the strontium-90 present after time t = N = q

The half life of strontium-90 =
`t_(1/2)=28.8 years`

Decay constant =
`\lambda`

`\lambda =(0.693)/(t_(1/2))=(0.693)/(28.8 years)=0.02406 years^(-1)`

`\ln N=\ln N_o -\lambda t`

`\ln q=\ln 3 - 0.02406 years^(-1)* t`

`0.02406 years^(-1)* t=\ln 3 - \ln q`

`0.02406 years^(-1)* t=\ln (3)/(q)`

`t=41.50 \ln (3)/(q)`

`e^t=((3)/(q))^(41.50)`

From the above expression we can see that t and q are inversely related to each other.