Question

The charcoal from ashes found in a cave gave 7.4 14C counts per gram per minute. Wood from the outer portion of a growing tree gives a comparable count of 15.3. The half-life of 14C is 5700 years.
How old are the ashes?
A) 3245 y
B) 5700 y
C) 5970 y
D) 9220 y
E) 5437 y

Answer 1

Answer:

C) 5970 y

Explanation:

Given;

initial amount of wood, N₀ = 15.3 cpm/g

remaining amount of wood (charcoal), N = 7.4 cpm/g

half life of carbon 14, t 1/2 = 5700 years

The age of the ashes can be calculated using the following formula;

$N = N_0(\frac{1}{2})^{\frac{t}{t_1_/_2} }\\\\(\frac{1}{2})^{\frac{t}{t_1_/_2} } = \frac{N}{N_0} \\\\(\frac{1}{2})^{\frac{t}{t_1_/_2} } = \frac{7.4}{15.3} \\\\(\frac{1}{2})^{\frac{t}{t_1_/_2} } = 0.48366\\\\t = t_{1/2} Log\frac{1}{2} (0.48366)\\\\t = \frac{t_{1/2}ln(0.48366)}{-ln(2)} \\\\t = t_{1/2}(1.0479)\\\\t = 5700(1.0479)\\\\t = 5973 \ years\\\\t = 5970 \ years(nearest \ ten)$

Therefore, the ashes are 5970 years