The rate of disintegration of a fixed quantity of a radioactive element can be increased by

$3.8$ days is the half-life period of a sample. After how many days, the sample will become $\frac{{1}}{{8}} \, th$ of the original substance

The normal activity of living carbon-containing matter is found to be about $15$ decays per minute 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 minute per gram of carbon. Estimate the approximate age (in $years$) of the Indus-Valley civilisation

$37$ Rutherford equals

A element used for radioactive carbon dating for more than $5600$ years is