Question

63Ni decays by a first-order process via the emission of a beta particle. The 63Ni isotope has a half-life of 100. years. How long will it take for 67% of the nickel to undergo decay?

Answer 1

Answer:

$t=57.8 y$

Explanation:

The time that will take for nickel to decay can be calculated using the decay equation:

$N_{(t)} = N_{0}e^{-\lambda t}$

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:

$\lambda = \frac{Ln(2)}{\tau}$        

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:

$0.67N_{0}= N_{0}e^{-\frac{ln(2)}{\tau} t}$

Finally, we just need to find t.

$t=-\frac{ln(0.67)}{ln(2)}100=57.8 y$

I hope it helps you!