Radioactive Decay Law

The time taken by the radioactive element to reduce to $1/e$ times is

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

A radioactive substance contains $10000$ nuclei and its half-life period is $20 \mathrm{days}$. The number of nuclei present at the end of $10 \mathrm{days}$ is

A radioactive element forms its own isotope after $3$ consecutive disintegrations. The particles emitted are

${}_{87}{}^{221}\mathrm{Ra}$ is a radioactive substance having half-life of $4 \mathrm{days}$. Find the probability that a nucleus undergoes decay after two half-lives.

A radioactive nuclide is produced at the constant rate of $\mathrm{n}$ per $\mathrm{second}$ (say, by bombarding a target with neutrons). The expected number $N$ of nuclei in existence $t \mathrm{seconds}$ after the number is $N_0$ is given by

What is the decay constant of radioactive substance whose half-life is $5 \mathrm{hours}$?

The half life for $\alpha -$decay of uranium ${}_{92}\mathrm{U}^{228}$ is $4.47\times {10}^8 \mathrm{yr}$. If a rock contains $60\%$ of original ${}_{92}\mathrm{U}^{228}$ atoms, then, its age is [Take $\log \left(6\right)=0.778\text{,} \log \left(2\right)=0.3$]

The activity of a radioactive sample is measured as ${\mathrm{N}}_0$ counts per minute at $\mathrm{t}=0$ and $\frac{{\mathrm{N}}_0}{e}$ counts per minute at $\mathrm{t}=5 \min .$ The time, (in minute) at which the activity reduces to half its value, is

A radioactive sample at any instant has its disintegration rate $5000$ disintegrations per minute. After $5 \mathrm{minutes}$, the rate is $1250$ disintegrations per minute. Then, the decay constant $\left({\mathrm{minute}}^{-1}\right)$ is

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

The activity of a radioactive sample is measured as $9750 \mathrm{counts} \mathrm{per} \mathrm{minute}$ at $t=0$ and as $975 \mathrm{counts} \mathrm{per} \mathrm{minute}$ at $\mathrm{T}=5 \min$. The decay constant is approximately

What is the age of an ancient wooden piece if it is known that the specific activity of ${\mathrm{C}}^{14}$ nuclide in its amount is $\frac{3}{5}$ of that in freshly grown trees? Given the half of ${\mathrm{C}}^{14}$ nuclide is $5570 \mathrm{yrs}$.

Half-lives of two radioactive substances $A$ and $B$ are, respectively, $20 \mathrm{minutes}$ and $40 \mathrm{minutes}$. Initially, the samples of $A$ and $B$ have the equal number of nuclei. After $80 \mathrm{minutes}$, the ratio of remaining number of $A$ and $B$ nuclei are

The activity of a radioactive sample is measured as $9750 \mathrm{counts} \mathrm{per} \mathrm{minute}$ at $t=0$, as $975 \mathrm{counts} \mathrm{per} \mathrm{minute}$ at $t=5 \min$. The decay constant is approximately

A freshly prepared radioactive source of half life $2 \mathrm{hr}$ emits radiation of intensity which is $64$ times the permissible safe level. The minimum time after which it would be possible to work safely with this source is

The half-life of radioactive Radon is $3.8 \mathrm{days}$. The time at the end of which ${\left(\frac{1}{20}\right)}^{\mathrm{th}}$ of the Radon sample will remain undecayed is (given ${\log }_{10}\mathrm{e}=0.4343$$)$

A radioactive substance has a half-life of four months. Three-fourth of the substance will decay in

If the half-life of a radioactive element is $3$ hours then after $9$ hours its activity of original will be

How long will it take for a radioactive sample to decrease to $10\%$ of its initial value, if its half-life is $22$ years?