Question

Nucleus A decays into the stable nucleus B with a half-life of 14.19 s. At t=0 s there are 1,891 A nuclei and no B nuclei. At what time will there be 832 B nuclei?

Answer 1

`N_(oA)=1891`

Using the decay formula:

`N=N_o((1)/(2))^{(T)/(T_(1/2))}`

Where:

`N=1891-832=1059`

So:

`\begin{gathered} 1059=1891((1)/(2))^{(T)/(14.19)} \\ (1059)/(1891)=((1)/(2))^{(T)/(14.19)} \\ 0.56=((1)/(2))^{(T)/(14.19)} \\ \end{gathered}`

Solve for T:

`\begin{gathered} log(0.56)=(T)/(14.19)log((1)/(2)) \\ T=14.19((log(0.56))/(log((1)/(2)))) \\ T\approx11.87s \end{gathered}`

Answer:

11.87 seconds