From the activity values and the decay constant, the mass of of Strontium in the sample is:
[tex]1.62 × 10^{-7}g[/tex]
The decay constant of an element is the probability of decay of a nucleus per unit time.
{λ = ln 2 / t1/2
where;
t1/2 is the half-life of the isotope.
The half-life is converted to seconds since the decay constant is asked in per seconds.
[tex]28.8 years = 28.8 × 3.156 × 10^{7} = 908928000 s \\ [/tex]
Hence;
[tex]λ = \frac{ln2}{90892800s} = 7.626 s^{-1}[/tex]
The activity of the element, A, the decay constant, λ and the number of nuclei, N are related as follows:
[tex]N = \frac{8.25 ×10^{5}}{7.626×10^{-10}} = 1.082 × 10^{15} [/tex]
Molar mass of Strontium-90 is 90 g.
1 mole of Strontium-90 contains 6.02×10^23 nuclei.
The mass, m of Strontium in the sample is calculated:
[tex]m = 1.082 × 10^{15} × \frac{90 g}{6.02 × 10^{23}} = 1.62 × 10^{-7}g \\ [/tex]
Therefore, the mass of of Strontium in the sample is:
[tex]1.62 × 10^{-7} \: g[/tex]
Learn more about decay constant at: https://brainly.com/question/17159453
