Question

After 42 days a 2.0 g sample of Copper contains only 0.25 g. what is the half life of copper?

Answer 1

Half-life of a substance is found by the next equation:

`N(t)\text{ = }N_0\cdot((1)/(2))^{(t)/(t0.5)}`

where:

N(t) is the quantity of the substance remaining

N0 is the initial quantity of the substance

t is the time elapsed

t0.5 is the half-life

Replacing with t = 42, N(t) = 0.25 and N0 = 2, we get:

`\begin{gathered} 0.\text{25 = 2}\cdot0.5^{(42)/(t0.5)} \\ (0.25)/(2)=0.5^{(42)/(t0.5)} \\ 0.125\text{ }=0.5^{(42)/(t0.5)} \\ \ln (0.125)\text{ = }(42)/(t0.5)\cdot\ln (0.5) \\ t_(0.5)=(42\cdot\ln (0.5))/(\ln (0.125)) \\ t_(0.5)=\text{14 days} \\ \end{gathered}`