The half life of free neutron is closest to

Important Questions on Atomic And Nuclear Physics

MEDIUM

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

The half-life of a particle of mass $1.6\times {10}^{-26} \mathrm{kg}$ is $6.9 \mathrm{s}$ and a stream of such particles is travelling with the $\mathrm{K}.\mathrm{E}.$ of a particle being $0.05 \mathrm{eV}$. The fraction of particles which will decay when they travel a distance of $1 \mathrm{m}$ is,

EASY

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

A radioactive nucleus $A$ with a half-life $T$, decays into a nucleus $B$. At $t=0$, there is no nucleus $B$. At some time $t$, the ratio of the number of $B$ to that of $A$ is $0\text{.}3$. Then, $t$ is given by: $\left(\text{Consider} {\log }_e\left(x\right)=\log \left(x\right)\right)$

MEDIUM

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

Two species of radioactive atoms are mixed in equal number. The disintegration of the first species is $\lambda$ and of the second is $\frac{\lambda }{3}$ . After a long time the mixture will behave as a species with mean life of approximately

MEDIUM

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

Half-lives of two radioactive elements $\mathrm{A}$ and $\mathrm{B}$ are $20 \mathrm{minutes}$ and $40 \mathrm{minutes}$, respectively. Initially, the samples have an equal number of nuclei. After $80 \mathrm{minutes}$, the ratio of decayed numbers of $\mathrm{A}$ and $\mathrm{B}$ nuclei will be:

MEDIUM

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

At a given instant, say $t=0,$ two radioactive substance $A$ and $B$ have equal activities. The ratio $\frac{R_B}{R_A}$ of their activities after time $t$ itself decays with time $t$ as $e^{-3t}.$ If the half-life of $A$ is $ln2,$ the half-life of $B$ is:

MEDIUM

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

A piece of wood from a recently cut tree shows $20$ decays per minute. A wooden piece of the same size placed in a museum (obtained from a tree cut many years back) shows $2$ decays per minute. If the half-life of ${\mathrm{C}}^{14}$ is $5730 \mathrm{years}$, then the age of the wooden piece placed in the museum is approximately
[This question was awarded a bonus and proper correction was made to avoid that]

EASY

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

A radioactive element has a rate of disintegration $10,000$ disintegrations per minute at a particular instant. After four minutes it becomes $2500$ disintegrations per minute. The decay constant per minute is

MEDIUM

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

A radio isotope ‘$X$’ with a half life $1.4\times {10}^9$ years decays to ‘$Y$’ which is stable. A sample of the rock from a cave was found to contain ‘$X$’ and ‘$Y$’ in the ratio $1:7$. The age of the rock is

HARD

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

Let $N_{\beta }$ be the number of $\beta$ particle emitted by $1 \mathrm{gram}$ of ${\mathrm{Na}}^{24}$ radioactive nuclei having a half life of $15 \mathrm{h}$. In $7.5 \mathrm{h}$, the number $N_{\beta }$ is close to $\left[N_{\mathrm{A}}=6.023\times {10}^{23} {\mathrm{mole}}^{-1}\right]$

EASY

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

The half-life of a radioactive substance is $30 \min$. The time (in minutes) taken between $40\%$ decay and $85\%$ decay of the same radioactive substance is

MEDIUM

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

Two radioactive substances $\mathrm{A}$ and $\mathrm{B}$ have decay constants $5\mathrm{\lambda }$ and $\mathrm{\lambda }$ respectively. At$\mathrm{t}=0$, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become ${\left(\frac{1}{\mathrm{e}}\right)}^2$ will be

MEDIUM

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At $t=0$ it was $1600$ counts per second and $t=8$ seconds it was $100$ counts per second. The count rate observed, as counts per second, at $t=6$ seconds is close to:

MEDIUM

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

Two radioactive materials $\mathrm{A}$ and $\mathrm{B}$ have decay constants $10\mathrm{\lambda }$ and $\mathrm{\lambda }$ , respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $\mathrm{A}$ to that of $\mathrm{B}$ will be $\frac{1}{e}$ after a time:

EASY

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

Radioactive material $A$ has decay constant $8\lambda$ and material $B$ has decay constant $\lambda$. Initially they have the same number of nuclei. After what time, the ratio of number of nuclei of material $A$ to that $B$ will be $\frac{1}{e}?$

MEDIUM

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

Half lives of two radioactive nuclei $\mathrm{A}$ and $\mathrm{B}$ are 10 minutes and 20 minutes, respectively. If, initially a sample has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be:

MEDIUM

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

The activity of a radioactive sample falls from $700{\mathrm{s}}^{-1}$ to $500{\mathrm{s}}^{-1}$ in $30$ minutes. Its half life is close to:

HARD

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

In a radioactive sample, ${\mathrm{ }}_{19}^{40}\mathrm{K}$ nuclei either decay into stable ${\mathrm{ }}_{20}^{40}\mathrm{C}\mathrm{a}$ nuclei with decay constant $4.5\times {10}^{-10}$ per year or into stable ${\mathrm{ }}_{18}^{40}\mathrm{A}\mathrm{r}$ nuclei with decay constant $0.5\times {10}^{-10}$ per year. Given that in this sample all the stable ${\mathrm{ }}_{20}^{40}\mathrm{C}\mathrm{a}$ and ${\mathrm{ }}_{18}^{40}\mathrm{A}\mathrm{r}$ nuclei are produced by the ${\mathrm{ }}_{19}^{40}\mathrm{K}$ nuclei only. In time $\mathrm{t}\times {10}^9$ years, if the ratio of the sum of stable ${\mathrm{ }}_{20}^{40}\mathrm{C}\mathrm{a}$ and ${\mathrm{ }}_{18}^{40}\mathrm{A}\mathrm{r}$ nuclei to the radioactive ${\mathrm{ }}_{19}^{40}\mathrm{K}$ nuclei is $99,$ the value of t will be : [Given $\mathrm{l}\mathrm{n}\mathrm{ }10=2.3$ ]

HARD

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

At some instant, a radioactive sample $S_1$ having an activity $5 \mu {\mathrm{Ci}}_{}$ has twice the number of nuclei as another sample $S_2$ which has an activity of $10 \mu {\mathrm{Ci}}_{}$ . The ratio of half lives of $S_1 \mathrm{a}\mathrm{n}\mathrm{d} S_2$ is

MEDIUM

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

In a radioactive decay chain, the initial nucleus is ${ }_{90}^{232}\mathrm{Th}$. At the end, there are $6$ $\alpha$-particles and $4\beta$-particles which are emitted. If the end nucleus is ${}_{\mathrm{Z}}^{\mathrm{A}}\mathrm{X}, A$ and $Z$ are given by:

HARD

Physics>Modern Physics>Atomic And Nuclear Physics>Discovery of Neutrons

An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive material of half-life $18$ days inside the laboratory. Tests revealed that the radiation was $64$ times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?