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?

Explanation:

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

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:

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:

Finally, we just need to find t.

I hope it helps you!

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