Mass defect and binding energy

The binding energy per nucleon of ${}^{209}_{83}Bi$ is ________ MeV.
[Take $m\left({}^{209}_{83}Bi\right)=208.980388$ u, $m_p=1.007825$ u, $m_n=1.008665$ u, 1 u = 931 MeV/c²]

Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a nucleus of mass number 10. If the binding energy per nucleon for the mass numbers 3, 4 and 10 are 5.6 MeV, 7.4 MeV and 6.1 MeV, respectively, then in the process, $\Delta Mc^2$ = ________ MeV.

Assuming the experimental mass of $^{12}_{\ 6}\mathrm C$ as 12 u, the mass defect of $^{12}_{\ 6}\mathrm C$ atom is ________ MeV/c².

(Mass of proton = 1.00727 u, mass of neutron = 1.00866 u, 1 u = 931.5 MeV/c² and c is the speed of the light in vacuum).

The energy released when $\dfrac7{17.13}$ kg of $^7_3\mathrm{Li}$ is converted into $^4_2\mathrm{He}$ by proton bombardment is $\alpha\times10^{32}$ eV. The value of $\alpha$ is ________. (Nearest integer)

(Mass of $^7_3\mathrm{Li}$ = 7.0183 u, mass of $^4_2\mathrm{He}$ = 4.004 u, mass of proton = 1.008 u and 1 u = 931 MeV/c² and Avogadro number = $6.0\times10^{23}$)

The energy released if hydrogen atoms are combined to form $^4_2\mathrm{He}$ is ________ MeV.

(Take binding energies per nucleon of $^2_1\mathrm H$ and $^4_2\mathrm{He}$ as 1.1 MeV and 7.2 MeV, respectively)

List-I shows various functional dependencies of energy ($E$) on the atomic number ($Z$). Energies associated with certain phenomena are given in List-II.

Choose the option that describes the correct match between the entries in List-I to those in List-II.

The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction ${}^{16}_{7}\mathrm N + {}^{4}_{2}\mathrm{He} \to {}^{1}_{1}\mathrm H + {}^{19}_{8}\mathrm O$ in a laboratory frame is $n$ (in MeV). Assume that ${}^{16}_{7}\mathrm N$ is at rest in the laboratory frame. The masses of ${}^{16}_{7}\mathrm N$, ${}^{4}_{2}\mathrm{He}$, ${}^{1}_{1}\mathrm H$ and ${}^{19}_{8}\mathrm O$ can be taken to be 16.006 $u$, 4.003 $u$, 1.008 $u$ and 19.003 $u$, respectively, where $1\,u = 930\ \mathrm{MeV}\,c^{-2}$. The value of $n$ is _____.

The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be $E_b^p$ and the binding energy of a neutron be $E_b^n$ in the nucleus.

Which of the following statement(s) is(are) correct?

Nucleus A is having mass number 220 and its binding energy per nucleon is 5.6 MeV. It splits in two fragments 'B' and 'C' of mass numbers 105 and 115. The binding energy of nucleons in 'B' and 'C' is 6.4 MeV per nucleon. The energy Q released per fission will be :

The Q-value of a nuclear reaction and kinetic energy of the projectile particle, $K_p$ are related as :

Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below :

$${}^2_1X+{}^2_1X={}^4_2Y$$

The binding energies per nucleon for ${}^2_1X$ and ${}^4_2Y$ are 1.1 MeV and 7.6 MeV respectively. The energy released in this process is ______ MeV.

A heavy nucleus $N$, at rest, undergoes fission $N \to P + Q$, where $P$ and $Q$ are two lighter nuclei. Let $\delta = M_N - M_P - M_Q$, where $M_P$, $M_Q$ and $M_N$ are the masses of $P$, $Q$ and $N$, respectively. $E_P$ and $E_Q$ are the kinetic energies of $P$ and $Q$, respectively. The speeds of $P$ and $Q$ are $v_P$ and $v_Q$, respectively. If $c$ is the speed of light, which of the following statement(s) is(are) correct?

Suppose a $\ce{^{226}_{88}Ra}$ nucleus at rest and in ground state undergoes α-decay to a $\ce{^{222}_{86}Rn}$ nucleus in its excited state. The kinetic energy of the emitted α particle is found to be 4.44 MeV. $\ce{^{222}_{86}Rn}$ nucleus then goes to its ground state by γ-decay. The energy of the emitted γ photon is ______ keV.

[Given: atomic mass of $\ce{^{226}_{88}Ra}$ = 226.005 u, atomic mass of $\ce{^{222}_{86}Rn}$ = 222.000 u, atomic mass of α particle = 4.000 u, 1 u = 931 MeV/c², c is speed of the light]

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)

Imagine that a reactor converts all given mass into energy and that it operates at a power level of $10^9$ watt. The mass of the fuel consumed per hour in the reactor will be : (velocity of light, c is $3\times10^8$ m/s)

The isotope $^{12}_{5}\mathrm B$ having a mass 12.014 u undergoes β-decay to $^{12}_{6}\mathrm C$. $^{12}_{6}\mathrm C$ has an excited state of the nucleus $(^{12}_{6}\mathrm C^*)$ at 4.041 MeV above its ground state. If $^{12}_{5}\mathrm B$ decays to $^{12}_{6}\mathrm C^*$, the maximum kinetic energy of the β-particle in units of MeV is ($1\ \mathrm u=931.5\ \mathrm{MeV}/c^2$, where $c$ is the speed of light in vacuum).

The electrostatic energy of $Z$ protons uniformly distributed throughout a spherical nucleus of radius $R$ is given by
$$E=\frac35\,\frac{Z(Z-1)e^2}{4\pi\varepsilon_0R}$$
The measured masses of the neutron, $^1_1\mathrm H$, $^{15}_{7}\mathrm N$ and $^{15}_{8}\mathrm O$ are 1.008665 u, 1.007825 u, 15.000109 u and 15.003065 u, respectively. Given that the radii of both the $^{15}_{7}\mathrm N$ and $^{15}_{8}\mathrm O$ nuclei are same, $1\ \mathrm u=931.5\ \mathrm{MeV}/c^2$ ($c$ is the speed of light) and $e^2/(4\pi\varepsilon_0)=1.44$ MeV fm. Assuming that the difference between the binding energies of $^{15}_{7}\mathrm N$ and $^{15}_{8}\mathrm O$ is purely due to the electrostatic energy, the radius of either of the nuclei is

($1\ \mathrm{fm}=10^{-15}$ m)

A fission reaction is given by $^{236}_{92}\mathrm U\to{}^{140}_{54}\mathrm{Xe}+{}^{94}_{38}\mathrm{Sr}+x+y$, where $x$ and $y$ are two particles. Considering $^{236}_{92}\mathrm U$ to be at rest, the kinetic energies of the products are denoted by $K_{Xe}$, $K_{Sr}$, $K_x$ (2 MeV) and $K_y$ (2 MeV), respectively. Let the binding energies per nucleon of $^{236}_{92}\mathrm U$, $^{140}_{54}\mathrm{Xe}$ and $^{94}_{38}\mathrm{Sr}$ be 7.5 MeV, 8.5 MeV and 8.5 MeV, respectively. Considering different conservation laws, the correct option(s) is(are)

The correct statement is

The kinetic energy (in keV) of the alpha particle, when the nucleus $^{210}_{84}\mathrm{Po}$ at rest undergoes alpha decay, is