Starting with a sample of pure ${}^{66}Cu$, $7/8$ of it decays into $Zn$ in $15\  minutes$ . The it decays into $Zn$ in $15\  minutes$ . The corresponding half-life is ................ $minutes$

The half-life of a radioactive nuclide is $100 \,hours.$ The fraction of original activity that will remain after $150\, hours$ would be :

Given below are two statements :

Statement $I:$ The law of radioactive decay states that the number of nuclei undergoing the decay per unit time is inversely proportional to the total number of nuclei in the sample.

Statement $II:$ The half life of a radionuclide is the sum of the life time of all nuclei, divided by the initial concentration of the nuclei at time $t =0$.

In the light of the above statements, choose the most appropriate answer from the options given below :

$10\, gm$ of radioactive material of half-life $15$ year is kept in store for $20$ years. The disintegrated material is ............$gm$

The relation between $\lambda $ and $({T_{1/2}})$ is (${T_{1/2}}=$ half life, $\lambda=$ decay constant)

The activity of a radioactive sample is $1.6\, curie$ and its half-life is $2.5 \,days$. Its activity after $10\, days$ will be .......... $curie$