Question

The half life of silicon -32 is 710 years. If 30 grams is present now, how much will be present in 300 years? (Round your answer to three decimal places.)

Answer 1

The half-life exponential decay equation is

`\begin{gathered} N(t)=N_0((1)/(2))^(\lambda) \\ \text{where} \\ \lambda=\frac{t}{t_{(1)/(2)}} \end{gathered}`

N_0 is the initial quantity of the substance, t_1/2 is the half-life and t is the time.

In our case,

`\begin{gathered} \lambda=(300)/(710)=(30)/(71) \\ N_0=30 \end{gathered}`

Therefore,

`N(300)=\frac{30}{2^{(30)/(71)}}=22.3833\ldots\approx22.383_{}`

The answer is 22.383 grams.