The half-life of ¹⁴C is 5,700 years. In a living organism the ¹⁴C content is a constant of 0.22 Bq/g. If an unknown sample contains a ¹⁴C activity of about Bq/g , approximately how old is the sample?

Question

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The formula for calculating the age of the sample is: t = (ln2 / λ) * (T + 0.693 / λ) where t is the age of the sample, λ is the decay constant (ln2 / half-life), T is the natural logarithm of the ratio of the ¹⁴C content in the sample to the content in a living organism, which is 0.22 Bq/g. Plugging in the values, we get: t = (ln2 / 5700) * (ln(11ea7c90_f22c_0fa6_9ab2_372ee12f3f22_TB1423_11 / 0.22)) t = 36.9 years Therefore, the age of the sample is approximately 36.9 years. The only choice that is close to this answer is C.

The Half-Life of 14C Is 5,700 Years

The Half-Life of ¹⁴C Is 5,700 Years