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

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 = $\lambda$

$\lambda =\frac{0.693}{t_{1/2}}=\frac{0.693}{28.8 years}=0.02406 years^{-1}$

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

$\ln q=\ln 3 - 0.02406 years^{-1}\times t$

$0.02406 years^{-1}\times t=\ln 3 - \ln q$

$0.02406 years^{-1}\times t=\ln \frac{3}{q}$

$t=41.50 \ln \frac{3}{q}$

$e^t=(\frac{3}{q})^{41.50}$

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