Answer:
49.8 hours
Step-by-step explanation:
Given data,
Initial amount of sodium-24 = I = 30 mg
Half life duration = d = 15 hours
Number of half life = n = ?
Remaining amount = A = 3 mg
The relation between the Initial amount, remaining amount and number of half life is calculated using: A = I(0.5)^n
By putting values in the equation above, we get
3 = 30(0.5)^n
3/30 = 0.5^n
1/10 = 0.5^n
Taking log on both side
ln(1/10) = ln(0.5)^n
-ln(10) = n*ln(0.5) as ln(1/x) = -ln(x)
-ln(10)/ln(0.5) = n
3.32 = n
n = 3.32
So it would take 3.32 number of half life for the 30 mg substance to be converted in 3 mg.
Duration of each half life d = 15 hours thus the total time required is
n*d
15*3.32
=> 49.8 hours
