Respuesta :
Explanation:
Formula for the first order decay is as follows.
[tex]ln(\frac{A}{A_{o}})[/tex] = -kt
where, A = activity at time t
[tex]A_{o}[/tex] = initial activity
k = decay constant
Hence, putting the given values into the above formula as follows.
k = [tex]\frac{ln(2)}{\text{half life}}[/tex]
= [tex]\frac{ln(2)}{8.0}[/tex]
= 0.086643 per day
Also, [tex]\frac{ln(6.22 \times 10^{17})}{9.95 \times 10^{8}} = -0.086643 \times t[/tex]
t = 32 days
Thus, we can conclude that it will take 32 days for the activity to drop to [tex]6.22 \times 10^{17}[/tex] [tex]\beta[/tex] particles per day.
