Question

The halflife of tritium (31H) is 12.3 y. 48.0-mg of tritium is released from a nuclear power plant during the course of a mishap.What mass of the nuclide will remain after 49.2 y? and then after 98.4 y?

Answer 1

Step 1

All radiation decay follows first order kinetics as follows:

`\text{A = A}_0xe^(-\lambda t)`

λ = decay constant

t = time taken

A0 = initially present mass

A = mass present after t time

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Step 2

Information provided:

12.3 y = half-life time = t 1/2

A0 = 48.0 mg

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Step 3

Procedure:

λ is calculated as follows:

`\begin{gathered} t_{(1)/(2)\text{ }}=\text{ }(ln2)/(\lambda) \\ \lambda\text{ = }\frac{ln\text{ 2}}{12.3\text{ years}}=\text{ 0.056 1/y} \end{gathered}`

Now,

From step 1:

`\begin{gathered} A\text{ = 48.0 mg x }e^{-0.056(1)/(years)x\text{ 49.2 years}} \\ A\text{ = 3.05 mg} \end{gathered}`

For t = 98.4 years => A = 0.194 mg

Answer:

What mass of the nuclide will remain after 49.2 y? 3.05 mg

And then after 98.4 y? 0.194 mg