Nuclei practice · Medium

In helium nucleus, there are

Cadmium rods are used in a nuclear reactor for

A sample of radioactive material decays simultaneously by two processes $A$ and $B$ with half-lives $\frac{1}{2}$ and $\frac{1}{4}$ hours respectively. For first half-hour, it decays with process $A,$ next one hour with process $B$ and for a further half an hour with both $A$ and $B.$ If originally there were ${N}_0$ nuclei, find the number of nuclei after 2 hours of such decay

The rest mass of an electron as well as that of positron is $0.51\,\,MeV$. When an electron and positron are annihilate, they produce gamma-rays of wavelength(s)

A nucleus ${ }_Z^A X$ has mass represented by $m(A, Z)$, If $m_p$ and $m_n$ denote the mass of proton and neutron respectively and BE the binding energy (in ${MeV}$ ) then.

In radioactive decay process, the negatively charged emitted $\mathrm{\beta } -$ particles are

The nuclei of two radioactive isotopes of same substance $\mathrm{A}^{236}$ and $\mathrm{A}^{234}$ are present in the ratio $4: 1$ in an ore obtained from Mars. Their half lives are $30 \mathrm{~min}$ and $60 \mathrm{~min}$ respectively. Both isotopes are alpha emitters and the activity of the isotope with half life 30 $\mathrm{min}$ is one Rutherford. Calculate after how much time (in min) their activities will become identical.

For a nucleus to be stable, the correct relation between neutron number $N$ and proton number $Z$ is

Which of the following nuclear reactions is not possible?

10 gm of a radioactive element is kept in a container. The element is $\beta$-active. Then after one half-life:

(molar mass of the substance is 100 gm, Avogadro's number $=6 \times 10^{23}$ per mole)

The electron emitted in beta radiation originates from

Atomic number of a nucleus is $Z$ and atomic mass is $M$. The number of neutron is

$M_x$ and $M_y$ denote the atomic masses of the parent and the daughter nuclei respectively in a radioactive decay. The $Q$-value of a $\beta^{-}$decay is $Q_1$ and that for a $\beta^{+}$decay is $Q_2$. If $m_e$ denotes the mass of an electron, then which of the following statement is correct?

In gamma ray emission from a nucleus

In which radiation atomic number and mass number are not
affected?

$_7{N^{14}}$ is bombarded with $_2\mathrm{H}{\mathrm{e}^4}$. The resulting nucleus is $_8{\mathrm{O}^{17}}$ with the emission of

In the chemical analysis of a rock the mass ratio of two radioactive isotopes is found to be $100: 1$. The mean lives of the two isotopes are $4 \times 10^9 {yr}$ and $2 \times 10^9 \mathrm{yr}$, respectively. If it is assumed that at the time of formation the atoms of both the isotopes were in equal proportion, the age of the rock $p \times 10^{10} \mathrm{yr}$, where the value of $p$ is ......... (Take, ratio of the atomic weights of the two isotopes is $1.02: 1$.)

When $_{88}\mathrm{R}{\mathrm{a}^{236}}$ decays in a series by emission of $3\,\mathrm{\alpha }$-particles and one $\mathrm{\beta }$-particle, isotope $X$ formed is

The binding energy of deuteron is 2.2 Mev and that of ${}_2H{e^4}$ is 28 Mev. If two deuterons are fused to form one ${}_2H{e^4}$ then energy released is

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

Plutonium decays with half-life of $\mathrm{24000 }\,\mathrm{yr}$. If plutonium is stored for $\mathrm{7200 }\,\mathrm{yr}$, the fraction of it that remains is

Which can pass through $20\,\,cm$ thickness of the steel

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

Assertion: In the process of nuclear fission, the fragments emit two or three neutrons as soon as they are formed and subsequently emit particles.

Reason: As the fragments contain an excess of neutrons over protons, emission of neutrons and particles bring their neutron/proton ratio to stable values.

Statement-I: If a heavy nucleus is split into two medium sized aprts, each of the new nuclei will have more binding energy per nucleon than the original nucleus.

Statement-II: Joining two light nuclei together to give a single nucleus of meidum size means more B.E per nucleon in the new nucleus.

Carbon $(Z=6)$ with mass number 11 decays to boron $(Z=5)$. (a) Is it a $\beta^{+}$-decay or a $\beta^{-}$-decay? (b) The half-life of the decay scheme is 20.3 minutes. How much time will elapse before a mixture of $90 \%$ carbon-11 and $10 \%$ boron-11 (by the number of atoms) converts itself into a mixture of $10 \%$ carbon-11 and $90 \%$ boron- 11?

When a proton, anti-proton annihilate ,the energy released is

A radioactive nucleus emits a beta particle. The parent and daughter nuclei are

A radio-isotope has a half-life of $5\,\,years$. The fraction of the atoms of this material that would decay in $15\,\,years$ will be

1 mg gold undergoes decay with 2.7 days half-life period,
amount left after 8.1 days is: