Question

An unknown radioactive substance has a half-life of 3.20 hours . If 22.8 g of the substance is currently present, what mass A0 was present 8.00 hours ago? Express your answer with the appropriate units.

Answer 1

Answer:

129 g

Explanation:

The radioactive decay of a substance can be represented through the following expression.

$A=A_{0}.e^{-k.t}$

where,

A is the amount of A at certain time t

A₀ is the initial amount of A

k is the rate constant

We can find k from the half-life (t1/2) using the following expression.

$t_{1/2}=\frac{ln2}{k} \\k=\frac{ln2}{t_{1/2}} =\frac{ln2}{3.20h} =0.217h^{-1}$

If 22.8 g of the substance is currently present, what mass A₀ was present 8.00 hours ago?

$A=A_{0}.e^{-k.t}\\22.8g = A_{0}.e^{-0.217h^{-1}\times 8.00h} \\A_{0}=129g$