Question

# Because of its chemical similarity to calcium, 90/38 Sr can collect in the bones and present a

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Because of its chemical similarity to calcium, $$\frac{90}{38}$$ Sr can collect in the bones and present a health risk.
Part A
What percentage of $$\frac{90}{38}$$ Sr present initially still exists after a period of 46.0y ?
Part B
What percentage of $$\frac{90}{38}$$ Sr present initially still exists after a period of 59.0y ?
Part C
What percentage of $$\frac{90}{38}$$ Sr present initially still exists after a period of 70.0y ?

2021-05-10

time $$t = 46$$ years
Exponential behavour of the number of undecayed nuclei
$$\displaystyle{N}={N}_{{o}}{e}^{{-\lambda}}{t}$$
$$\displaystyle{\frac{{{N}}}{{{N}_{{o}}}}}={e}^{{-\lambda}}{t}$$
half life of Sr is 28.9 years
decay constant $$\displaystyle\lambda={\frac{{{0.693}}}{{{t}^{{\frac{{1}}{{2}}}}}}}$$
$$=\frac{0.693}{28.9}$$
$$=0.0239$$
$$\displaystyle{\frac{{{N}}}{{{N}_{{o}}}}}={e}^{{-{0.0239}\cdot{46}}}$$
$$\displaystyle={0.3331}$$
$$=33.31\%$$
time $$t = 59$$ years
$$\displaystyle{\frac{{{N}}}{{{N}_{{o}}}}}={e}^{{-{0.0239}\cdot{59}}}$$
$$\displaystyle={0.2441}$$
$$=24.41\%$$
time $$t=70$$ years
$$\displaystyle{\frac{{{N}}}{{{N}_{{o}}}}}={e}^{{-{0.0239}\cdot{70}}}$$
$$=0.1877$$
$$=18.77\%$$