1. Calculate the following information about the radioactive isotope of radium,
ID: 969033 • Letter: 1
Question
1. Calculate the following information about the radioactive isotope of radium, Ra-226. The initial concentration of it in the water is 0.3 femtomolar (0.3 x 10^-15 mol/L).
a. What is the daughter of Ra-226
b. Given the half lives of Ra-226 and it's daughter, calculate the decay constants ?, for each species in days-1
c. What is the initial activity (A) of Ra-226 in the system? How about it's daughter?
d. What do you expect the equilibrium activity of the daughter isotope will be (assume a closed system)? Why?
e. How long will it take for the activity of the daughter isotope to reach 90% of the value as predicted in part d? what is its concentration at this time?
Explanation / Answer
a)222Rn
b)half life of Ra-226=1600 years=0.693/decay constant of Ra-226 , half life of 222Rn=3.8 days=0.693/decay constant of 222Rn
0.693/1600*365=1.2 *10^(-6) day -1 0.693/3.8= 0.18 day -1
c)
no of atoms per gram of radium=avagadro no/atomic mass=2.6645*10^(21)
initial activity = decay constant * no of atoms per gram=1.2 *10^(-6)*2.6645*10^(21)=3.2*10^(15) dis/day
no of atoms per gram of radium=avagadro no/atomic mass=2.7*10^(21)
initial activity = decay constant * no of atoms per gram=0.18*2.7*10^(21)=0.486 dis/day
d)
activity of daughter will be equal to activity of parent
long half life of parent = small decay constant of parent
Ab/Aa=decay constant of b/decay constant of b - decay constant of a
since decay constant of b>>decay constant of a so activity of daughter will be equal to activity of parent
e)A at any time=A[1- exp(-decay constant*t)]
0.1=exp(-decay constant*t)
-2.302=-decay constant*t , t=2.302/0.18=12.79 days
concentration=N = No e - decayconstant*t
=2.7*10^(21) exp(-0.18*12.79)
= 1.62*10^(21) atoms
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.