Half-life is the time taken for the concentration of the substance to reduce by 50%. The original sample of strontium had a mass of 1.6 gms. Thus, option d is correct.
The half-life of any radioactive substance is the time period at which the concentration will get reduced to half the initial amount. The initial mass of Sr-90 is calculated as,
[tex]N(t) = N_{0} (\dfrac{1}{2})^{ \frac{t }{t 1/2}}[/tex]
Given,
Quantity of the remaining substance N (t) = 0.40 gm
Initial radioactive substance quantity [tex]N_{0}[/tex] =?
Time duration (t) = 56 years
Half-life = 28 years
Substituting values above:
[tex]\begin{aligned} 0.40 &= N_{0} (\dfrac{1}{2}) ^{{\frac{56}{28}}\\\\0.40 &= N_{0} (\dfrac{1}{2})^{2}\end{aligned}[/tex]
= 1.6 gm
Therefore, option d. the initial mass of Sr is 1.6 gm.
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