Answer to Question #170960 in Physics for gigi

Question

An isotope of carbon, ₆C¹⁴, has a half-life of 5730 y. How much of a 4.0-g sample of the isotope will remain after 22,920 y?

Answer 1

Let’s use the formula for radioactive decay:

$$N=N_0e^{-\lambda t},$$ $$N=N_0e^{-\dfrac{0.693}{T_{1/2}} t},$$ $$N=4.0\ g\cdot e^{-\dfrac{0.693}{5730\ y}\cdot22920\ y}=0.25\ g.$$