Answer:
[tex]t=57.8 y[/tex]
Explanation:
The time that will take for nickel to decay can be calculated using the decay equation:
[tex] N_{(t)} = N_{0}e^{-\lambda t} [/tex]
Where:
N(t): is the quantity of Ni that still remains after a time t,
N(0): is the initial quantity of Ni
t: is the time
λ: is the decay constant of Ni
The decay constant can be calculated using the half-life of Ni:
[tex] \lambda = \frac{Ln(2)}{\tau}[/tex]
Here:
τ is the half-life (τ = 100 y)
Now, we can write N(t) in terms of N(0), because we know that nickel decay 67% after t time, in other words: N(t)=N(0)*0.67.
Therefore, we can rewrite the decay equation:
[tex] 0.67N_{0}= N_{0}e^{-\frac{ln(2)}{\tau} t} [/tex]
Finally, we just need to find t.
[tex]t=-\frac{ln(0.67)}{ln(2)}100=57.8 y[/tex]
I hope it helps you!
