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Leni [432]
4 years ago
15

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 w

as present 8.00 hours ago? Express your answer with the appropriate units.
Chemistry
1 answer:
Nonamiya [84]4 years ago
4 0

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}

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

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

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