Nuclei practice · Mixed difficulty

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

Choose incorrect statement:

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:

If a particle is being added to the nucleus of an atom but not changing its chemical properties. Then, these particles are

A radioactive $\beta$-emission. A detector records $n \beta$-particles in $2 s$ and by next $2 s$ (accumulatively) it records $1.1 n \beta$-particle. Number of $\beta$-particles recorded by detector after a long time, is

In nuclear reactions, we have the conservation of

If ${M_0}$ is the mass of an oxygen isotope $_8{\mathrm{O}^{17}}$ , ${M_p}\,\,and\,\,{M_n}$ are the masses of a proton and a neutron, respectively, the nuclear binding energy of the isotope is

Assertion: In a decay atom number of daughter nucleus reduces by 2 from the parent nucleus.

Reason:An Q-particle carries four units of mass.

The fossil bone has a $^{14}\mathrm{C}{:^{12}}\mathrm{C}$ ratio, which is $\left[ {\frac{1}{{16}}} \right]$ of that in a living animal bone. If the half-life of $^{14}\mathrm{C}$ is $\mathrm{5730 }\,\mathrm{yr}$, then the age of the fossil bone 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:

If $\mathrm{M}_{\mathrm{o}}$ is the mass of isotope ${ }_5^{12} \mathrm{B}, \mathrm{M}_{\mathrm{p}}$ and $\mathrm{M}_{\mathrm{n}}$ are the masses of proton and neutron, then nuclear binding energy of isotope is:

Ratio of the wavelengths of first line of Lyman series and first line of Balmer series is

The correct sequence of the increasing wavelength of the given radiation sources is

Two nuclei have their mass numbers in the ratio of 1 : 27. The ratio of their volume is

${}_{\mathrm{92}}^{\mathrm{238}}\mathrm{U}$ emits 8 $\alpha \mathrm{ - }$ particle and 6 $\beta -$ particles. The neutron/proton ratio in the product nucleus is

The subatomic particles proton and neutron fall under the group of

An artificial radioactive decay series begins with unstable $_{94}^{241}Pu$. The stable nuclide obtained after eight $\alpha -$ decays and five $\beta -$ decays is

Fusion process, like combining two deuterons to form a He nucleus are impossible at ordinary temperatures and pressure. This reasons for this can be traced to the fact

The radius of a spherical nucleus as measured by electron scattering is 3.6 fm. What is the likely mass number of the nucleus?

For nuclear reaction, select correct statement for released energy

A nuclear fusion reaction is given by $4\left( {{}_2^4He} \right) \to {}_8^{16}O$. If atomic mass of He is 4.0026 amu and that of O is 15.9994 amu then the Q-value of the reaction will be approximately

Consider the following two statements $A$ and $B$ identify the correct answer given
A: Nuclear density is same for all nuclei
B:Radius of the nucleus $R$ and its mass the number $A$ are related as $\sqrt A \propto {R^{1/6}}$