Write nuclear reaction equations for :
(i) $\alpha$ - decay of ${}_{88}^{226}Ra$                         (ii) $\alpha$ - decay of  ${}_{94}^{242}Pu$(iii) ${\beta }^{-}$ - decay of ${}_{15}^{32}P$                        (iv) ${\beta }^{-}$ - decay of ${}_{83}^{210}Bi$(v) ${\beta }^{+}$ - decay of ${}_6^{11}C$                         (vi) ${\beta }^{+}$ - decay of ${}_{43}^{97}Tc$(vii) Electron capture of ${}_{54}^{120}Xe$

The normal activity of living carbon-containing matter is found to be about 15 decays per ute for every gram of carbon. This activity arises from the small proportion of radioactive ${}_6^{14}C$ present with the stable carbon isotope ${}_6^{12}C$. When the organism is dead, its interaction with the atmosphere (which maintains the above equilibrium activity) ceases and its activity begins to drop. From the known half-life ( 5730 years) of ${}_6^{14}C$, and the measured activity, the age of the specimen can be approximately estimated. This is the principle of ${}_6^{14}C$ dating used in archaeology. Suppose a specimen from Mohenjodaro gives an activity of 9 decays per ute per gram of carbon. Estimate the approximate age of the Indus-Valley civilisation.