Question

7.2.45 The charcoal from a trokiled in the volcanic eruption that formed a crater contained 43.5% of the carbon-14 found in living matter. If the half-life of carbon-14 is 6700 years, about how old is the crater? The crater is about years old (Round to the nearest year as needed)

Answer 1

Given Half life = 5700. years we know. KE Plt) = . Po e -0 Equation of decay. Pot initial amount of carbon-14. Po amount will remain P(5700) = ginen (half 2. after half life) put t=5700 in in o 5700k. P15700) = Po e stook given [ P15700) = Po Do २ =% e stook. е. ㅗ 2 11 е. A a=lna ent] 5700k dog ent X 5700.

Now at Hime ť s amount of carbon-k ů of inital amount. 43.5 percent Plt) = 43.5% of Po i-e. Plt) = 0.435 Po en la in o put a K = 9 PLH = 0.435 Po 5700 en/2 t. 57oo 0.435 %= %o e Inyt stoo 0.435 e en 5700 et = = ln 0.435. 5700 ln (0.435) 5700 *(-0.8324) -0.693. t = en(!). t = 6902:11 years 6902 year old about The crator is