Two isotopes of lanthanum, one stable (`""^(139)La`) and another active (`""^(138)Lalpha`) are having a half-life of `10^(10)` years. I f the atoms of active isotope are 0.1% of the stable isotope, then estimate the activity of `""^(138) La` with 0.5 kg of `""^(139)La`

Explanation

To estimate the activity of the radioactive isotope \(^{138}\text{La}\) with 0.5 kg of stable \(^{139}\text{La}\), we can follow these steps:

### Step 1: Determine the number of moles of \(^{139}\text{La}\)
The molar mass of lanthanum is approximately \(139 \, \text{g/mol}\). To find the number of moles in 0.5 kg (or 500 g) of \(^{139}\text{La}\):

\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{500 \, \text{g}}{139 \, \text{g/mol}} \approx 3.60 \, \text{mol} \]
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