For a radioactive material,the half-life is $10$ minutes. If initially there are $600$ nuclei,the time taken (in minutes) for the disintegration of $450$ nuclei is:

At time $t = 0$,$N_1$ nuclei of decay constant $\lambda_1$ and $N_2$ nuclei of decay constant $\lambda_2$ are mixed. The decay rate of the mixture is:

$A$ source contains two phosphorus radionuclides $_{15}^{32} P \left(T_{1/2} = 14.3 \ d\right)$ and $_{15}^{33} P \left(T_{1/2} = 25.3 \ d\right)$. Initially,$10\%$ of the decays come from $_{15}^{33} P$. How long must one wait until $90\%$ of the decays come from $_{15}^{33} P$?

The half-life period of a radioactive sample is $T$. If a fraction $x$ disintegrates in time $t$,what fraction will decay in time $\frac{t}{2}$?

Two radioactive samples $A_1$ and $A_2$ have decay constants $10\lambda_0$ and $\lambda_0$ respectively. If they initially contain the same number of nuclei,find the ratio of the number of undecayed nuclei after time $t = 1/(9\lambda_0)$.

$A$ radioactive element has a half-life of $15$ years. What is the fraction that will decay in $30$ years?