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

`t=57.8 y`

Step-by-step 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 = (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^{-(ln(2))/(\tau) t}`

Finally, we just need to find t.

`t=-(ln(0.67))/(ln(2))100=57.8 y`

I hope it helps you!