Half Life, Mean Life

The expression for the average life of a radionuclide that shows its relationship with the half – life would be:

What is the probability that a radioactive nucleus will not have decayed after a time equal to twice its half-life?

If $N_0$ is the initial mass of a substance with half-life $t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=5 years$, then the amount of substance left after $15 years$ is

At some instant the ratio of the amount of two radioactive elements is $2:1$. If their half-lives respectively are $12$ hours and $16$ hours, then after two days, the ratio of the amount of two substances is

$Uranium-238$ decays to $Thorium-234$ with half-life $5\times {10}^9\mathrm{ }\mathrm{y}\mathrm{r}$ . The resulting nucleus is in the excited state and hence further emits $\mathrm{\gamma }$ -rays to come to the ground state. It emits $\mathrm{20 }\mathrm{\gamma }$ -rays per second. The emission rate will drop to $\mathrm{5 }\mathrm{\gamma }$-rays per second in

After $280$ days, the activity of a radioactive sample is $600 \mathrm{dps}$. The activity reduces to $300 \mathrm{dps}$ after another $140$ days. The half-life of the radioactive sample is

A radioactive element has a half-life of $3.6 \mathrm{days}$. At what time will it be left ${\left(\frac{1}{32}\right)}^{\mathrm{nd}}$ undecayed?

The decay constant of a radioactive substance is $\lambda$. The life and mean life of substance are, respectively, given by

The half lives of radioisotopes $P^{32}$ and $P^{33}$ are $20$ days and $30$ days, respectively. These radio isotopes are mixed in the ratio of $4:1$ of their atoms. If the initial activity of the mixed sample is $7 \mathrm{mCi}$, then the activity of the mixed isotopes after $60$ days will be $\dots \dots \mathrm{mCi}.$

A rock which is $10,000$ years old initially contains only Uranium nuclei. Uranium is radioactive which decays into $\mathrm{Pb}$ with a half life period $t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$. At present, the ratio of Uranium and $\mathrm{Pb}$ nuclei in the rock is found to be $1:31$. The half life period $t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ of Uranium is,

Half life of a radioactive substance is $1 \min$ . It is produced at a constant rate $R_0={10}^8$ nuclei per sec. How soon after (in $\min$, to the nearest integer), the beginning of production will its activity be equal to $7.5\times {10}^7$ disintegration per sec.

If the half life of a radio active is $T,$ then the fraction that would remain after a time $\frac{T}{2}$ is

The half life period of a radioactive element $X$ is same as the mean life time of another radioactive element $Y.$ Initially both of them have the same number of atoms. Then :-

A rock which is $10,000$ years old, initially contains only Uranium nuclei. Uranium is radioactive which decays into $\mathrm{Pb}$ with a half life period $t_{1/2}$. At present time the ratio of Uranium and $\mathrm{Pb}$ nuclei in the rock is found to be $1:31$. The half life period $t_{1/2}$ of Uranium is :

If the half-life of a radioactive substance is $33$ years $3$ months, what is the mean life? Round the answer to the nearest integer.

The decay constant of a radioactive substance is $\lambda =1.386\times {10}^{-10} {\mathrm{s}}^{-1}$. What is the half-life of it in Giga seconds? (${\log }_{e}2=0.693$)

The half-life of radioactive radon is $3.8$ days. The time at the end of which ${\left(\frac{1}{20}\right)}^{th}$ of the radon sample will remain undecayed, is :-

If the decay or disintegration constant of a radioactive substance is $\lambda ,$ then its half life and mean life are respectively

The half life of a substance is $20 \min$. What is the time interval between $10\%$ decay and $55\%$ decay (approximate)?

The decay constant of a radioactive sample is $\lambda$. The half-life and the average life of the sample are respectively