This problem uses radioactive isotopes. I need to find the amount of grams after 4000 years. I'm given:
Isotope:14-C
Half-life (years): 5715
Initial Quantity: 15 g
Amount After 4000 Years: ?? g
Also unsure as to starting this one.
Use the following two formulae:
$\displaystyle {\lambda} = \frac{ln2}{t_{1/2}}$
$\displaystyle A(t) = A_0e^{-\lambda t}$
Where:
- $\displaystyle \lambda$ = Decay Constant
- $\displaystyle t_{1/2}$ = half life
- $\displaystyle A(t)$ = Amount left at time t
- $\displaystyle A_0$ = Amount at t=0
- $\displaystyle t$ = time.
Let t denote the time measured in years, A_0 the initial amount and A(t) the amount after t years. Then A(t) is given by:
$\displaystyle A(t)=A_0 \cdot e^{k\cdot t}$ where k is a constant which you have to calculate first.
You already know: If the initial value is A_0 then $\displaystyle A(5715) = \frac12 A_0$. That means:
$\displaystyle \frac12 A_0 = A_0 \cdot e^{k \cdot 5715}$ . Solve for k. I've got $\displaystyle k \approx -0.0001212856$
Now calculate A(4000) with $\displaystyle A_0 = 15\ g$