Answer:
a) T= 3.82 days b) t=1.05 days
Explanation:
(a)
The radioactive decay model is given by the mathematical expression that defines the exponential decrease, which can be expressed as:
N = N0 · 0.5 t/T
Beaing
T = half life in days
t = days
N0= Number of atoms initially
N = Number of remaining atoms
N(t) = N0 (0.5)t/T
For the data of the problem, it is necessary to know:
N(t)/ N0 = %N/100
So
0.58 = (0.5)3/T
I apply logarithm to clear T
log(0.58) = (3/T) log(0.5)
T = 3 log(0.5) / log(0.58) days = 3.82 days
(b)
I use the previous formulas. So I have left
0.15 = (0.5)t/T = (0.5)t/3.82
log(0.15) = (t/3.82) log(0.5)
t=3.82log(0.15)/ log(0.15)
t=1.05 days
