Question

If 100. g of gold-198 decays to 6.25g in 10.8 days, what is the half-life of gold-198?

Answer 1

Given data

*The amount of gold-198 is N = 100 g

*The amount of gold decays is n = 6.25 g

*The given number of days is T = 10.8 days

The expression for the radioactivity decay is given as

$N=n(0.5)^{\frac{T}{t}}$

*Here t is the half-life period

Substitute the values in the above expression as

$\begin{gathered} 100=6.25(0.5)^{\frac{10.8}{t}} \\ t=2.7\text{ days} \end{gathered}$