Mass Defect & Binding Energy

The binding energy per nucleon of ${}_{83}^{209}Bi$ is _______ MeV.

[Take $m({}_{83}^{209}Bi) = 208.980388$u, $m_p = 1.007825$ u, $m_n = 1.008665$ u, $1$u $= 931$MeV$/c^{2}$]

Given below are two statements:

Statement I: For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon.

Statement II: For all elements, nuclei with less binding energy per nucleon transforms to nuclei with greater binding energy per nucleon.

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

Assuming the experimental mass of ${}_{6}^{12}C$ as $12u$, the mass defect of ${}_{6}^{12}C$ atom is $\_\_\_\_\_\ \text{MeV/c}^{2}$. (Mass of proton $= 1.00727\text{u}$. mass of neutron $= 1.00866\text{u}, 1\text{u} = 931.5\text{MeV/c}^{2}$ and c is the speed of the light in vacuum).

The binding energy for the following nuclear reactions are expressed in MeV.

${}_{2}\text{He}^{3} + {}_{0}\text{n}^{1} \rightarrow {}_{2}\text{He}^{4} + 20\text{MeV}$

${}_{2}\text{He}^{4} + {}_{0}\text{n}^{1} \rightarrow {}_{2}\text{He}^{5} - 0.9\text{MeV}$

If $\mathrm{X_3, X_4, X_5}$ denote the stability of ${}_{2}\text{He}^{3}, {}_{2}\text{He}^{4}$ and ${}_{2}\text{He}^{5}$, respectively, then the correct order is:

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): The binding energy per nucleon is found to be practically independent of the atomic number A, for nuclei with mass numbers between 30 and 170.

Reason (R): Nuclear force is long range. In the light of the above statements, choose the correct answer from the options given below:

The energy equivalent of $1\text{ g}$ of substance is:

Binding energy of a certain nucleus is $18 \times 10^{8}\text{ J}$. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

The mass defect in a particular reaction is $0.4\text{ g}$. The amount of energy liberated is $n \times 10^{7}\text{ kWh}$, where $n =$ __________. (speed of light $= 3 \times 10^{8}\text{ m/s})$

If $\mathrm{M_O}$ is the mass of an oxygen isotope ${}_{8}\text{O}^{17}$ and $\mathrm{M_p}$ and $\mathrm{M_N}$ are the mass of proton and mass of neutron respectively, then the nucleus binding energy of the isotope is

If $M_0$ is the mass of isotope ${}_{5}^{12}B, M_p$ and $M_n$ are the masses of proton and neutron, then nuclear binding energy of isotope is:

The atomic mass of ${}_{6}\text{C}^{12}$ is $12.000000\text{ u}$ and that of ${}_{6}\text{C}^{13}$ is $13.003354\text{ u}$. The required energy to remove a neutron from ${}_{6}\text{C}^{13}$, if mass of neutron is $1.008665\text{ u}$, will be:

The mass of proton, neutron and helium nucleus are respectively $1.0073\,u, 1.0087\,u$ and $4.0015\,u$. The binding energy of helium nucleus 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 binding energy per nucleon is practically independent of the atomic number for nuclei of mass number in the range 30 to 170.

Reason R: Nuclear force is short ranged.

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

Nucleus A having $Z = 17$ and equal number of protons and neutrons has $1.2\text{ MeV}$ binding energy per nucleon.

Another nucleus $\text{B}$ of $Z = 12$ has total 26 nucleons and $1.8\text{ MeV}$ binding energy per nucleons. The difference of binding energy of $\text{B}$ and $\text{A}$ will be _____________ $\text{MeV}$.

For a nucleus ${}_{\text{Z}}^{\text{A}}\text{X}$ having mass number $\text{A}$ and atomic number $\text{Z}$

A. The surface energy per nucleon $(b_{\text{s}}) = -a_1 A^{2/3}$.

B. The Coulomb contribution to the binding energy $\text{b}_{\text{c}} = -a_2 \frac{Z(Z-1)}{A^{4/3}}$

C. The volume energy $\text{b}_{\text{v}} = a_3 A$

D. Decrease in the binding energy is proportional to surface area.

E. While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons. ( $a_1, a_2$ and $a_3$ are constants)

Choose the most appropriate answer from the options given below:

From the given data, the amount of energy required to break the nucleus of aluminium ${}_{13}^{27}$Al is __________ x $\times$ 10$-$3 J.

Mass of neutron = 1.00866 u

Mass of proton = 1.00726 u

Mass of Aluminium nucleus = 27.18846 u

(Assume 1 u corresponds to x J of energy)

(Round off to the nearest integer)

The energy equivalent of 0.5 g of a substance is:

Find the Binding energy per nucleon for ${}_{50}^{120}Sn$. Mass of proton mp = 1.00783 U, mass of neutron mn = 1.00867 U and mass of tin nucleus mSn = 119.902199 U. (take 1U = 931 MeV)

Imagine that a reactor converts all given mass into energy and that it operates at a power level of 109 watt. The mass of the fuel consumed per hour in the reactor will be: (velocity of light, c is 3×108 m/s)

How does the Binding Energy per nucleon vary with the increase in the number of nucleons?

The mass of a ${}_{3}^{7}Li$ Li nucleus is 0.042 u less than the sum of the masses of all its nucleons. The binding energy per nucleon of ${}_{3}^{7}Li$ nucleus is nearly

The above is a plot of binding energy per nucleon $E_b,$ against the nuclear mass $M; A, B, C, D, E, F$ correspond to different nuclei. Consider four reactions:

$(i)\ \ A + B \rightarrow C + \varepsilon \quad (ii)\ \ C \rightarrow A + B + \varepsilon$

$(iii)\ \ D + E \rightarrow F + \varepsilon \quad (iv)\ \ F \rightarrow D + E + \varepsilon,$

where $\varepsilon$ is the energy released? In which reactions is $\varepsilon$ positive?

If M(A; Z), Mp and Mn denote the masses of the nucleus ${}_{Z}^{A}X,$ proton and neutron respectively in units of u (1 u = 931.5 MeV/c2) and BE represents its bonding energy in MeV, then

This question contains Statement- 1 and Statement- 2. Of the four choices given after the statements, choose the one that best describes the two statements:

Statement- 1:

Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion. Statement- 2:

For heavy nuclei, binding energy per nucleon increases with increasing $Z$ while for light nuclei it decreases with increasing $Z.$

A nucleus ${}_{Z}^{A}X$ has mass represented by M(A, Z). If Mp and Mn denote the mass of proton and neutron respectively and B.E. the binding energy in MeV, then

If $M_O$ is the mass of an oxygen isotope ${}_{8}O^{17}, M_p$ and $M_N$ are the masses of a proton and neutron respectively, the nuclear binding energy of the isotope is

If M(A; Z), Mp and Mn denote the masses of the nucleus ${}_{Z}^{A}X,$ proton and neutron respectively in units of u (1 u = 931.5 MeV/c2) and BE represents its bonding energy in MeV, then

The mass of proton is 1.0073 u and that of neutron is 1.0087 u (u = atomic mass unit). The binding energy of ${}_{2}^{4}$ He is

(Given helium nucleus mass $\approx$ 4.0015 u.)

If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should

Mn and Mp represent the mass of neutron and proton respectively. An element having mass M has N neutrons and Z protons, then the correct relation will be

The binding energy per nucleon is maximum in case of

The energy equivalent of one atomic mass unit is

The mass of $\alpha$-particle is

The average binding energy of a nucleon inside an atomic nucleus is about