Class 12 Physics Modern Physics Nuclei

A piece of wood from the ruins of an ancient building was found to have a $C_{14}$ activity of $12$ disintegration per minute per gram of its carbon content. The $C_{14}$ activity of the living wood is $16$ disintegration per minute per gram. How long ago did the tree, from which the wooden sample came, di? Given half-life of $C_{14}$ is $5760$ years.

Solution: Rate of disintegration in old wood sample of C-14 radioactive atms is $12$ atoms per min gm. Initially rate of distintegration of $C−14$ when the tree was live $=16$ atoms per min per gm.

$T_{1/2}$ of C-14 nuclei $=5760$ years

According to radioactive decay law

$=N_{0}e_{−λt}orR=R_{0}e_{−λt}$

$12=16e_{−λt}⇒e_{λt}=1216 $

$g_{e}e_{λt}=g_{e}34 $

$λt=g_{e}34 $

$t=λ2.303×g_{10}34 (∵λ=T_{1/2}0.6931 )$

$=0.69312.303×(g4−g3 )×5760 year$

$∴t=0.69312.303(0.6060−0.4771)5760 =2391.20years$

$T_{1/2}$ of C-14 nuclei $=5760$ years

According to radioactive decay law

$=N_{0}e_{−λt}orR=R_{0}e_{−λt}$

$12=16e_{−λt}⇒e_{λt}=1216 $

$g_{e}e_{λt}=g_{e}34 $

$λt=g_{e}34 $

$t=λ2.303×g_{10}34 (∵λ=T_{1/2}0.6931 )$

$=0.69312.303×(g4−g3 )×5760 year$

$∴t=0.69312.303(0.6060−0.4771)5760 =2391.20years$

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