A zircon crystal contains the isotope (half-life ) which decays to

PHYSICS · Subjective · CBSE · Physics · Nuclei · Nuclei

Problem

A zircon crystal contains the isotope

_{92}^{238}\text U

(half-life

4.5\times10^{9}\,\text{yr}

) which decays to

_{82}^{206}\text{Pb}

. In a

1.00\,\text{mg}

sample of the crystal, chemical analysis shows

0.60\,\text{mg}

^{238}\text U

and

0.25\,\text{mg}

^{206}\text{Pb}

. Geological studies indicate that

0.05\,\text{mg}

of the lead was present when the crystal formed. (i) Calculate the number ratio of radiogenic

^{206}\text{Pb}

atoms to the remaining

^{238}\text U

atoms. (ii) Hence estimate the age of the crystal. (Take atomic masses equal to the mass numbers.)