Question

The half-life of carbon-14 is 5,730 years. How many grams of parent material will remain from a 120-gram sample of carbon-14 after 2 half-lives?

90

60

30

15

Answer 1

After one half-life . . . 1/2 of the total parent material

After another half-life . . . 1/2 of the half remains = 1/4 of the total original parent

If the original parent is 120 grams, then (1/4 x 20) = 30 grams remains
after 2 half-lives. It makes no difference what the substance is, or
how long its half-life is.

Answer 2

`t_{(1)/(2)}=5730\\ N_0=120\ g\\ t=2t_{(1)/(2)}=2\cdot5730=11460\\ N(t)=?\\\\ N(t)=N_0\left((1)/(2)\right)^{\frac{t}{t_{(1)/(2)}}}\\ N(11460)=120\cdot\left((1)/(2)\right)^{(11460)/(5730)}\\ N(11460)=120\cdot\left((1)/(2)\right)^2\\ N(11460)=120\cdot(1)/(4)\\ N(11460)=30\ g`