We’re being asked **to determine how many grams of ^{206}Hg 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:

$\overline{){\mathbf{ln}}{\mathbf{\left[}\mathbf{N}\mathbf{\right]}}_{{\mathbf{t}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{ln}}{\mathbf{\left[}\mathbf{N}\mathbf{\right]}}_{{\mathbf{o}}}}$

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 ^{210}Pb remaining

**Step 2. **Calculate the mass of ^{210}Pb that decayed

**Step 3. **Calculate moles ^{210}Pb decayed

**Step 4. **Calculate moles ^{206}Hg produced

**Step 5.** Calculate mass ^{206}Hg produced

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

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the First Order Half Life concept. You can view video lessons to learn First Order Half Life. Or if you need more First Order Half Life practice, you can also practice First Order Half Life practice problems.

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