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  4. The half-life of C14 radioactive is 5760 yr. After how much time will 200 mg C14 sample be reduced to 25 mg?

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Q. The half-life of $ {{C}^{14}} $ radioactive is 5760 yr. After how much time will 200 mg $ {{C}^{14}} $ sample be reduced to 25 mg?

Rajasthan PETRajasthan PET 2006

Solution:

$ {{t}_{1/2}}=5760\,yr $
$ N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}} $
$ 25=200{{\left( \frac{1}{2} \right)}^{n}} $
$ \frac{25}{200}={{\left( \frac{1}{2} \right)}^{n}} $
$ \frac{1}{8}={{\left( \frac{1}{2} \right)}^{n}} $
$ {{\left( \frac{1}{2} \right)}^{3}}={{\left( \frac{1}{2} \right)}^{n}} $
$ n=3 $ $ =3\times 5760\,yr $
$ =17280\,yr $