## S1
Don't forget to change to moles.
To determine the age of the rock sample, we can use the formula for radioactive decay:
$$N_{U}(t) = N_{U,0}\left(e^{-ln(2)\frac{t}{t_{0.5}}}\right)$$
$$N_{Pb}(t) = N_{U,0}\left(1-e^{-ln(2)\frac{t}{t_{0.5}}}\right) + N_{Pb,0}$$
Consider $\frac{N_{Pb}(t)-N_{Pb,0}}{N_{U}(t)}$
$$\frac{N_{Pb}-N_{Pb,0}}{N_{U}}=1-e^{-ln(2) \frac{t}{t_{0.5}}}$$
$$\ln\left(1-\frac{N_{Pb}-N_{Pb,0}}{N_{U}}\right)= -\ln(2) \frac{t}{t_{0.5}}$$
$$-\ln\left(1-\frac{N_{Pb}-N_{Pb,0}}{N_{U}}\right)\frac{1}{ln(2)} t_{0.5}= t$$
Watch out, that $N_{U}$ is the original amount of Mothernucleid (so for A1 you need to calculate that first)
### A1
**a)** 4.32 billion yr
**b)** 2.21 billion yr
**c)** Beta decay: $$n \to e^{-}+ p^{+} + \bar \nu$$
### A2
**a)**1.71 billion yr
**b)**0.39 billion yr
### A2
**a)**1.71 billion yr
**b)**0.39 billion yr