# Problem: 210Pb has a half-life of 22.3 years and decays to produce 206Hg. If you start with 7.50 g of 210Pb, how many grams of 206Hg will you have after 17.5 years?

###### FREE Expert Solution

We’re being asked to determine how many grams of 206Hg will you have after 17.5 years.

Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the integrated rate law for first-order reactions is:

where:

[N]t = concentration at time t

k = decay constant

t = time

[N]0 = initial concentration.

We go through the following steps to solve the problem:

Step 1. Calculate the mass of 210Pb remaining

Step 2. Calculate the mass of 210Pb that decayed

Step 3. Calculate moles 210Pb decayed

Step 4. Calculate moles 206Hg produced

Step 5. Calculate mass 206Hg  produced

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###### Problem Details

210Pb has a half-life of 22.3 years and decays to produce 206Hg. If you start with 7.50 g of 210Pb, how many grams of 206Hg will you have after 17.5 years?