UPSC Combined Geo-Scientist, Mains · 2018 · Mains Paper I

Q1(g). Radiocarbon age

Question

A wooden article of old age shows 40% as much ¹⁴C activity as a fresh piece of wood. Calculate the age of the article. (t_(1/2) of ¹⁴C = 5760 years)

The calculated age is 7.61×10³ years, using the half-life specified in the paper.

Activity is proportional to the number of undecayed atoms: A=A₀e^{-λ t}, where λ=ln 2/t_(1/2).
Here A/A₀=0.40. Thus t=5760/(ln 2)ln 1/0.40=7614 years.
This assumes equivalent original specific activity and no subsequent exchange or contamination. Use the supplied half-life rather than replacing it with a different tabulated value.

The full model answer

As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.

CoversRadiocarbon ageRadioactive decay