Carbon-14 decays by beta emission to stable isotope of nitrogen. Carbon-14 half-life of 5700 years(i) A pure sample of carbon-14 initially contains 8.0 × 1020 atoms. Calculate number of atoms of carbon and of nitrogen present in sample after 11 400 years?

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Answer 1 · 2018-03-04T04:08:24

#2*10^20# atoms

Since #""^14C# has a half life of #5700# years, then after #11400# years, it has elapsed #2# half lives.

If #n# is the number of half-lives elapsed, then there will be #100/(2^n)%# of the substance left. (Source: https://en.wikipedia.org/wiki/Half-life)

So, after #2# half-lives, there will be

#100/(2^2)%#

#=100/4%#

#=25%#

of the original amount left.

Since there was #8*10^20# carbon-14 atoms in the beginning, there will be #25%*8*10^20=2*10^20# carbon-14 atoms left after #11400# years.