97.17 years will be required until the 90sr is reduced to 1.0 ppm
Calculation :
Radiactive decays are always follow first order kinetics .
[tex]t_{1/2}[/tex] = 28.8 yr
for first order reaction,
kt = ln([A]0/[A]t)
where k = rate constant
t = time
[A]0 =initial concentration
[A]t = concentration at time t
And half cycle [tex]t_{1/2}[/tex] = 0.693/k
28.8 yr = 0.693/k
k = 0.024yr⁻¹
[A]0 = 10.3 ppm
[A]t = 1.0 ppm
k*t = ln([A]0/[A]t)
t * 0.024 = ln(10.3/1.0)
t= 2.332/0.024
t = 97.17 yr
Half-life in radioactivity, the time interval required for half of the nuclei in a radioactive sample to decay (spontaneously transform into other types of nuclei by releasing particles and energy), or equivalently, the time required for decay times Every second of interval radioactivity ...
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