Answer:
After 3 hours there is left 22.5 grams of radioactive material.
Step-by-step explanation:
We can calculate the mass of radioactive material remaining after 3 hours, by using the decay equation:
[tex]N_{t} = N_{0}*e^{-\lambda t}[/tex] (1)
Where:
[tex]N_{0}[/tex]: is the initial mass = 180 g
[tex]N_{t}[/tex]: is the remaining mass after time t
λ: is the decay constant
The decay constant is given by:
[tex] \lambda = \frac{ln(2)}{t_{1/2}} [/tex]
Where [tex]t_{1/2}[/tex] = 1 h.
By entering λ into equation (1) we hve:
[tex] N_{t} = N_{0}*e^{-\frac{ln(2)}{t_{1/2}} t} [/tex]
[tex] N_{t} = 180 g*e^{-\frac{ln(2)}{1 h} 3 h} = 22.5 g [/tex]
Therefore, after 3 hours there is left 22.5 grams of radioactive material.
I hope it helps you!
