The ratio of ^14C/^12C in a piece of wood is 1/8 part that of atmosphere.

Question

The ratio of \(\frac {^{14}C}{^{12}C}\) in a piece of wood is \(\frac {1}{8}\) part that of atmosphere. If half life of \(^{14}C\) is 5730 years, the age of wood sample is ….. years.

Answer 1

Correct answer is : 17190

\(\lambda t = ln \cfrac {(^{14}C/^{12}C)_{atmosphere}}{(^{14}C/^{12}C)_{wood\,sample}}\)

As per the question,

\(\cfrac {(^{14}C/^{12}C)_{wood}}{(^{14}C/^{12}C)_{atmosphere}} = \frac {1}{8}\)

So, \(\lambda t = ln 8\)

\(\frac {In \, 2}{t _ {1/2}}t= ln 8\)

\(t = 3 \times t _ {1/2} = 17190\,years\)