From the calculations, the half life of the material is 6.5 days.
The term radioactivity has to do with the spontaneous disintegration of a specie.
Uisng the formula;
N=Noe^-kt
N= amount at time t = 0.135 Ci or 4.995 ×10^9 Bq
No = amount initially present = 1.75 x 10^12 Bq
k = rate constant = ?
t = time taken = 55 days
Hence;
4.995 ×10^9 = 1.75 x 10^12e^-55k
4.995 ×10^9/1.75 x 10^12 = e^-55k
2.85 * 10^-3 = e^-55k
ln2.85 * 10^-3 = -55k
k = ln2.85 * 10^-3/-55
k = 0.1066 day-1
Half life = 0.693/ 0.1066 day-1
= 6.5 days
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