Radioactivity Questions

The photon of hard gamma radiation knocks a proton out of ${}_{12}^{24}\text{Mg}$ nucleus to form:

The energy spectrum of $\beta$ -particles [number $N(E)$ as a function of $\beta$ -energy $E$ ] emitted from a radioactive source is:

A radioactive element gets spilled over the floor of a room. Its half-life period is $30\text{days}$. If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room?

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

In gamma ray emission from a nucleus:

The intensity of gamma radiation from a given source is $I$. On passing through $36\text{ mm}$ of lead, it is reduced to $I/8$. The thickness of lead which will reduce the intensity to $I/2$ will be:

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

When ${}^{238}\text{U}$ nucleus originally at rest, decays by emitting an alpha particle having a speed $u$, the recoil speed of the residual nucleus is:

A radioactive sample at any instant has its disintegration rate $5000\text{disintegrations per minute}$. After $5\text{minutes}$, the rate is $1250\text{disintegrations per minute}$. Then, the decay constant (per minute) is:

A nucleus with $Z=92$ emits the following in a sequence: $\alpha ,\alpha ,{\beta }^{-},{\beta }^{-},\alpha ,\alpha ,\alpha ,\alpha ,{\beta }^{-},{\beta }^{-},\alpha ,{\beta }^{+},{\beta }^{+},\alpha$. The $Z$ of the resulting nucleus is:

Which of the following cannot be emitted by radioactive substance during their decay?

A radioactive nucleus (initial mass number $A$ and atomic number $Z$) emits $3\alpha$ -particles and $2$ positrons. The ratio of number of neutrons to that of protons in the final nucleus will be:

The half life of a radioactive substance is $20\text{minutes}$. The approximate time interval $(t_2-t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it has decayed and time $t_1$ when $\frac{1}{3}$ of it had decayed is: