Respuesta :
78.78 g out of 250 g of Thorium-234 would remain after 40 days.
Explanation:
All radioactive samples are unstable in nature and so they will be decaying with time. So the equation of disintegration of the radioactive element is given as
[tex]N=N_{0}e^{-kt}[/tex]
So N is the mass of the radioactive element at time t and [tex]N_{0}[/tex] is the mass of the radioactive element at initial stage. Here k is the disintegration constant and t is the time.
We can determine the disintegration constant from the half life term of any element.
[tex]Half life = \frac{0.693}{k}[/tex]
So, [tex]k = \frac{0.693}{Half life}[/tex]
Since, the half life time of thorium-234 is known to be 24 days. Then, the disintegration constant is
[tex]k = \frac{0.693}{24}=0.028875[/tex] [tex]days^{-1}[/tex]
As the given questions have the initial mass [tex]N_{0}[/tex] as 250 g and t is given as 40 days, then the mass after 40 days will be
[tex]N = 250 * e^{-0.02887*40}= 250 * e^{-1.1548}=78.78 g.[/tex]
Thus, 78.78 g of thorium-234 would remain after 40 days.
