If in the case of a radioisotope the value of half-life $(T_{1/2})$ and decay constant $(\lambda)$ are identical in magnitude, then their value should be

The half-life of radium-$226$ is $1620$ years. The time taken to convert $10 \ g$ of radium to $1.25 \ g$ is ......... years.

To determine the half-life of a radioactive element,a student plots a graph of $\ln|dN(t)/dt|$ versus $t$. Here $dN(t)/dt$ is the rate of radioactive decay at time $t$. If the number of radioactive nuclei of this element decreases by a factor of $p$ after $4.16 \ \text{years}$,the value of $p$ is

If $1 \ \mu g$ of radium $(^{226}Ra)$ has disintegrated for $500$ years,how many alpha particles will be emitted per second?

The decay of a radioactive element follows first-order kinetics. As a result:

The amount of $_{53}I^{128}$ $(t_{1/2} = 25 \ minutes)$ left after $50 \ minutes$ will be