Explanation:
Initial mass of the isotope 90-Sr in baby= 1.00 μg
Formula used :
[tex]N=N_o\times e^{-\lambda t}\\\\\lambda =\frac{0.693}{t_{\frac{1}{2}}}[/tex]
where,
[tex]N_o[/tex] = initial mass of isotope
N = mass of the parent isotope left after the time, (t)
[tex]t_{\frac{1}{2}}[/tex] = half life of the isotope = 28.1 years
[tex]\lambda [/tex] = rate constant
[tex]N=N_o\times e^{-(\frac{0.693}{t_{1/2}})\times t}[/tex]
a) Time taken by the sample, t = 18 years
[tex]N=1.00 \mu g\times e^{-\frac{0.693}{28.1 years}\times 18 years}[/tex]
[tex]N = 0.6415 \mu g[/tex]
0.6415 μg will remain after 18 years.
b) Time taken by the sample, t = 70 years
[tex]N=1.00 \mu g\times e^{-\frac{0.693}{28.1 years}\times 70 years}[/tex]
[tex]N = 0.1779\mu g[/tex]
0.1779 μg will remain after 70 years.
