Answer:
2.23 days
Explanation:
Given that;
N=Noe^-kt
Where;
N= number of radioactive nuclei present at time =t
No= number of radioactive nuclei originally present
k = decay constant
t = time taken
But k = ln2/T
Where T is the half life of the radioactive nuclei
Hence;
NA= Noe^-ln2t/TA (1)
NB= Noe^-ln2t/TB (2)
But NA =2.44NB
2.44NB = Noe^-ln2t/TA (3)
NB= Noe^-ln2t/TB (4)
Divide (3) by (4)
2.44NB/NB = Noe^-ln2t/TA/Noe^-ln2t/TB
2.44 = e^-ln2t/TA + ln2t/TB
Taking natural logarithm of both sides
ln2.44 = -ln2t/TA + ln2t/TB
Given that TB = 1.14 days
TA= -ln2t(ln2.44 -ln2t/TB )^-1
TA= -(2.079) (0.892 - 2.079/1.14)^-1
TA = 2.23 days
