Answer : The correct option is, 0.200 g
Solution :
As we know that the radioactive decays follow first order kinetics.
First we have to calculate the rate constant of a samarium-146.
Formula used :
Putting value of in this formula, we get the rate constant.
Now we have to calculate the original amount of samarium-146.
The expression for rate law for first order kinetics is given by :
where,
k = rate constant =
t = time taken for decay process =
a = initial amount of the samarium-146 = 205 g
a - x = amount left after decay process = ?
Putting values in above equation, we get the value of initial amount of samarium-146.
Therefore, the amount left of the samarium-146 is, 0.200 g