Question

Carbon-14 is a radioisotope that is used for dating biological organisms. The half-life of C-14 is 5730 years. When a one-gram sample of carbon from fresh peat is measured for radioactivity, 900 beta decays are recorded every hour. A one-gram sample of carbon is obtained from a peat deposit and is measured for radioactivity. If 113 beta decays are observed every hour, how many half-lives of C-14 have passed since the deposit was formed?

A. 1/8 B.3 C.113 D.8

Approximately how old is the peat deposit?

A.716 years B.17190 years C.5617 years D.45840 years

Another one-gram sample is obtained from a different peat deposit at a different site. If 14 beta decays are measured every hour, about how old is this sample?

A.80220 years B.5716 years C.34380 years D.366720 years

Answer 1

Given data Half-life of C14, -5730 years Number of B decays for fresh peat per hour, N-900 Number of B decays for sample peat per hour, N 113 If the number of half-lives passed isn, then consider the following expression. Substitute the values in above expression. 113-900 2 Hence, the number of half-lives passed is 3 Therefore, option (B) is correct.

Consider the age (A) of the peat Substitute the values in the above expression. A 3x5730 -17190 years Hence, the peat is 17190 years old Therefore, option (B) is correct Given that, the number of β decays for another sample is.14 Apply equation (1) to calculate the number of half years passed 14-900

Apply equation (2) to calculate the age of the sample. A 6x 5730 34380 years Hence, the sample is 34380 years old. Therefore option (C) is correct.