Nuclei practice · Mixed difficulty

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then:

The energy equivalent to a kilogram of matter is about

In helium nucleus, there are

A radioactive nucleus of mass $M$ emits a photon of frequency $v$ and the nucleus recoils. The recoil energy will be

In the following nuclear reaction ${x}$ stands for $n \rightarrow p+e^{-}+x$

A radioactive substance with decay constant of $0.5 / {s}$ is being produced at a constant rate of 50 nuclei per second. If there are no nuclei present initially, the time (in second) after which 25 nuclei will be present is:

If $\lambda$ is decay constant and $N$ the number of radioactive nuclei of an element , then the decay rate ($R$) of that element is

Neutron decay in free space is given as follows
$_0{n^1}{ \to _1}{\mathrm{H}^1} + { - _1}{e^0} + \,\,[\,]$ Then the parenthesis represents a

In the reaction $_1^2H + \,_1^3\,\,H \to _2^4He + \,_0^1\,\,n$ if the binding energies of $_1^2H,_1^3\,H$ and $_2^4He$ are respectively $a,b$ and $c$ (in $MeV$), then the energy (in $MeV$) released in this reaction is

The nucleus ${}_{48}C{d^{115}}$ after two successive ${\beta ^ - }$ decays will give

Nueclius density:

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$

Assertion A: The nuclear density of nuclides ${ }_5^{10} \mathrm{~B}$, ${ }_3^6 \mathrm{Li},{ }_{26}^{56} \mathrm{Fe},{ }_{10}^{20} \mathrm{Ne}$ and ${ }_{83}^{209} \mathrm{Bi}$ can be arranged as $\rho_{\mathrm{Bi}}^{\mathrm{N}}>\rho_{\mathrm{Fe}_{\mathrm{N}}}^{\mathrm{N}}>\rho_{\mathrm{Ne}_{\mathrm{N}}}^{\mathrm{N}}>\rho_{\mathrm{B}}^{\mathrm{N}}>\rho_{\mathrm{Li}}^{\mathrm{N}}$

Reason $\mathbf{R}$ : The radius $R$ of nucleus is related to its mass number $A$ as $R=R_0 A^{1 / 3}$, where $R_0$ is a constant.

In the light of the above statements, choose the correct answer from the options given below

Two deuterons undergo nuclear fusion to form a Helium nucleus. Energy released in this process is (given binding energy per nucleon for deuteron = 1.1 MeV and for helium = 7.0 MeV)

A radioactive nucleus $_Z^AX$ undergoes spontaneous decay in the sequence
$_Z^AX{ \to _{Z - 1}}B{ \to _{Z - 3}}C{ \to _{Z - 2}}D,$ where $Z$ is the atomic number of element $X$. The possible decay particles in the sequence are

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

When the number of nucleons in nuclei increase, the binding energy per nucleon

The example of nuclear fusion is

Assuming that the mass of proton is nearly equal to mass of neutron the minimum kinetic energy in $10^1 \mathrm{eV}$ of a neutron for inelastic head on collision with a ground state hydrogen atom at rest is -

Assertion: Density of all the nuclei is same.

Reason: Radius of nucleus is directly proportional to the cube root ofmass number.

A radioactive sample decays with an average-life of $20 \mathrm{~ms}$. A capacitor of capacitance $100 \mu \mathrm{F}$ is charged to some potential and then the plates are connected through a resistance $R$. What should be the value of $R / 40$ so that the ratio of the charge on the capacitor to the activity of the radioactive sample remains constant in time?

An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8 : 27. The ratio of the radii of the nuclei (assumed to be spherical) is :

The energy released in the fusion of $2 \mathrm{~kg}$ of hydrogen deep in the sun is $\mathrm{E}_{\mathrm{H}}$ and the energy released in the fission of $2 \mathrm{~kg}$ of ${ }^{235} \mathrm{U}$ is $\mathrm{E}_{\mathrm{U}}$. The ratio $\frac{\mathrm{E}_{\mathrm{H}}}{\mathrm{E}_{\mathrm{U}}}$ is approximately :

(Consider the fusion reaction as ${4}_1^1 \mathrm{H}+2 \mathrm{e}^{-} \rightarrow{ }_2^4 \mathrm{He}+2 \mathrm{v}+6 \gamma+26.7 \mathrm{~M~eV}$, energy released in the fission reaction of ${ }^{235} \mathrm{U}$ is $200 \mathrm{~M~eV}$ per fission nucleus and $\mathrm{N}_{\mathrm{A}}=6.023 \times 10^{23}$)

Assertion: In ${U}_{\mathrm{235}}$ fission reaction neutrons are required to be slowed down.
Reason: The probability of capture of slow moving neutrons is high for ${U}_{\mathrm{235}}$.

Nuclear fission can be explained based on

If a proton and anti-proton come close to each other and annihilate, how much energy will be released

If radius of the ${ }_{13}^{27} A l$ nucleus is taken to be $R_{A l},$ then the radius of ${ }_{52}^{125} {Te}$ nucleus is:

The following deuterium reactions and corresponding reaction energies are found to occur
${ }^{14} {N}(d, p){ }^{15} {N}, Q=8.53 \,\mathrm{MeV}$
${ }^{15} {N}(d, \alpha){ }^{13} {C}, Q=7.58 \,\mathrm{MeV}$
${ }^{13} {N}(d, \alpha){ }^{11} {B}, Q=5.16\, \mathrm{MeV}$
(The notation ${ }^{14} {N}(d, p){ }^{15} {N}$ represent the reaction ${ }^{14} {N}+d \rightarrow{ }^{15} {N}+p$ ${ }_2^4 {He}=4.0026 \mathrm{~amu} ; { }_1^2 {H}=2.014 \,\mathrm{amu} ; { }_1^1 {H}=1.0078 \mathrm{~amu}; n=1.0087 \mathrm{~amu} \,(1 \mathrm{~a m u}=931 \mathrm{~MeV}).$ The $Q$ values of the reaction ${ }^{11} {B}(\alpha, n){ }^{14} {N}$ is:

Choose the best option for binding energy/nucleon if nuclear energy is released in fission. Binding energy is

Following statements related to radioactivity are given below:
(A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.
(B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time.
(C) Slope of the graph of loge (no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time $\left( \tau \right).$
(D) Product of decay constant $\left( \lambda \right)$ and half-life time $\left( {{T_{1/2}}} \right)$ is not constant.
Choose the most appropriate answer from the options given below:

Decay constant of radium is $\lambda$. By a suitable process its compound radium bromide is obtained. The decay constant of radium bromide will be