The sample of a radioactive substance has $10^6$ nuclei. Its half life is $20 \,s$. The number of nuclei that will be left after $10 \,s$ is nearly …… $\times 10^5$

If $'f^{\prime}$ denotes the ratio of the number of nuclei decayed $\left(N_{d}\right)$ to the number of nuclei at $t=0$ $\left({N}_{0}\right)$ then for a collection of radioactive nuclei, the rate of change of $'f'$ with respect to time is given as:

$[\lambda$ is the radioactive decay constant]

A certain radioactive material can undergo three different types of decay, each with a different decay constant $\lambda_1$, $\lambda_2$ and $\lambda_3$ . Then the effective decay constant is

Let $N_{\beta}$ be the number of $\beta $ particles emitted by $1$ gram of $Na^{24}$ radioactive nucler (half life $= 15\, hrs$) in $7.5\, hours$, $N_{\beta}$ is close to (Avogadro number $= 6.023\times10^{23}\,/g.\, mole$)

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