A green plant contains radioactive ${}^{14}\mathrm{C}\text{ and }{}^{12}\mathrm{C}$ isotope. If in a sample of dead old wood of this plant $2.5\times {10}^{-6}{ \mathrm{mol}}^{14}\mathrm{C}\text{ and }7.5\times {10}^{-6}{ \mathrm{mol}}^{14} \mathrm{N}$ are present then calculate value of Z. Assuming all ‘N’ is obtained due to disintegration of ${ }^{14}C$.

Where $Z=\frac{Ageofwood\left(t\right)}{Halflifeof{}^{14}Cisotope\left(t_{1/2}\right)}$