Binding Energy

Q.

In a reactor, 2 kg of ₉₂U²³⁵ fuel is fully used up in 30 days. The energy released per fission is 200 MeV. Given that the Avogadro number, N = $6.023\times {10}^{26}$per kilo mole and $1eV=1.6\times {10}^{-19}J$. close to

1. a) 60 MW

2. b) 54 MW

3. c) 125 MW

4. d) 35 MW

Q. The potential energy of an electron in hydrogen atom is $-6.8\text{eV}$. Indicate in which excited state, the electron is present?

1. $1\text{st}$
2. $2\text{nd}$
3. $3\text{rd}$
4. $4\text{th}$

Q. Nuclear binding energy is the energy released during the hypothetical formation of the nucleus by the condensation of individual nucleons. Thus, binding energy per nucleon =$\frac{\text{Total binding energy}}{\text{Number of nucleons}}$ For example, the mass of hydrogen atom is equal to the sum of the masses of a proton and an electron. For other atoms, the atomic mass is less than the sum of the masses of protons, neutrons and electrons present. This difference in mass, termed as mass defect, is a measure of the binding energy of protons and neutrons in the nucleus. The mass-energy relationship postulated by Einstein is expressed as: $\Delta E=\Delta m{c}^2$
Where $\Delta E$ is the energy liberated, $\Delta m$ is the loss of mass, and c is the speed of light.
In the reaction ${}_1^{2}H{+}_1^{3}H{\to }_2^{4}He{+}_0^{1}n$, if binding energies ${}_1^{2}H{,}_1^{3}H\text{and}{}_2^{4}He$ are respectively a, b and c (in MeV), then the energy released in this reaction is:

1. $a+b+c$
2. $a+b-c$
3. $c-a-b$
4. $c+a-b$

Q.

$C{u}^{64}$ (half life = 12.8 hours) decays by ${\beta }^{⊝}-emission$ (38%), ${\beta }^{\oplus }-emission$(19%), and electron capture (43%). Write the decay products and calculate partial half lives for each of the decay processes.
(IIT-JEE, 2002)

1. 33.70 hr, 67.41 hr and 29.78 hr
2. 29.78 hr , 33.70 hr and 67.41 hr
3. 67.41 hr, 33.70 hr and 29.78 hr
4. 29.78 hr, 67.41 hr and 33.70 hr

Q. In how many ways, can the two-dimensional close packed structure be generated?

1. 1
2. 2
3. 3
4. 4

Q. The binding energy of an element is 64 MeV. If the binding energy per nucleon is 6.4 MeV, then the number of nucleons are 10.

1. True
2. False

Q. The amount of U-235require per day to run a power house of capacity 15 mw (efficiency of nuclear reactor 75 per .assume that energy librated by fusion of 1 mev is

Q. Nuclear binding energy is the energy released during the hypothetical formation of the nucleus by the condensation of individual nucleons. Thus, binding energy per nucleon =$\frac{\text{Total binding energy}}{\text{Number of nucleons}}$ For example, the mass of hydrogen atom is equal to the sum of the masses of a proton and an electron. For other atoms, the atomic mass is less than the sum of the masses of protons, neutrons and electrons present. This difference in mass, termed as mass defect, is a measure of the binding energy of protons and neutrons in the nucleus. The mass-energy relationship postulated by Einstein is expressed as: $\Delta E=\Delta m{c}^2$
Where $\Delta E$ is the energy liberated, $\Delta m$ is the loss of mass, and c is the speed of light.
In the reaction ${}_1^{2}H{+}_1^{3}H{\to }_2^{4}He{+}_0^{1}n$, if binding energies ${}_1^{2}H{,}_1^{3}H\text{and}{}_2^{4}He$ are respectively a, b and c (in MeV), then the energy released in this reaction is:

1. $a+b+c$
2. $a+b-c$
3. $c-a-b$
4. $c+a-b$

Q. Assertion :Nuclear binding energy per nucleon is in the order ${}_4^{9}Be{>}_3^{7}Li{>}_2^{4}He$. Reason: Binding energy per nucleon increases linearly with difference in number of neutrons and protons.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. The electrons identified by quantum numbers n and l
(i) n=4, l=1
(ii) n=4, l=0
(iii) n=3, l=2
(iv) n=3, l=1
can be placed in order of increasing energy from the lowest to highest, as

1. (iv) < (ii) < (iii) <(i)
2. (ii) < (iv) < (i) < (iii)
3. (i) < (iii) < (ii) < (iv)
4. (iii) < (i) < (iv) < (ii)

Q. If two protons and two neutrons are brought extremely close together to form a single, bound particle, the energy released in the process will be equal to:

1. There might or might not be any energy released
2. The binding energy of helium nucleus
3. There will be no energy released
4. The mass-energy of an alpha particle.

Q. Nuclear binding energy is the energy released during the hypothetical formation of the nucleus by the condensation of individual nucleons. Thus, binding energy per nucleon =$\frac{\text{Total binding energy}}{\text{Number of nucleons}}$ For example, the mass of hydrogen atom is equal to the sum of the masses of a proton and an electron. For other atoms, the atomic mass is less than the sum of the masses of protons, neutrons and electrons present. This difference in mass, termed as mass defect, is a measure of the binding energy of protons and neutrons in the nucleus. The mass-energy relationship postulated by Einstein is expressed as:
$\Delta E=\Delta m{c}^2$
Where $\Delta E$ is the energy liberated, $\Delta m$ is the loss of mass, and c is the speed of light.

$MP$ and $Mn$ are masses of a proton and a neutron respectively. For a nucleus, its binding energy is $B$ and it contains $Z$ protons and $N$ neutrons, the correct relation for this nucleus if $C$ is velocity of light is:

1. $M(N,Z)=N{M}_n+Z{M}_p-B{C}^2$
2. $M(N,Z)=N{M}_n+Z{M}_p+B{C}^2$
3. $M(N,Z)=N{M}_n+Z{M}_p-\frac{B}{C^2}$
   
4. $M(N,Z)=N{M}_n+Z{M}_p+\frac{B}{C^2}$

Q. Natural nitrogen is 99.63% ${}^{14}N$ with mass 14.00307 amu and 0.37% ${}^{15}N$, with mass number 15.00011 amu. Which isotope is more stable, ${}^{14}N$ or ${}^{15}N$ ?
Plan Binding energy per nucleon$=\frac{△m\left(amu\right)\times 931}{numberofnucleons}$
Isotope with larger binding energy per nucleon is more stable.

1. $7.695$ MeV
2. $2.995$ MeV
3. $8.8695$ MeV
4. None of these

Q. The total number of neutrons present in 54 mL $H_{2}O\left(l\right)$ are:

1. $3N_A$
2. $30N_A$
3. $24N_A$
4. none of these

Q. Calculate the binding energy of the oxygen isotope ${}_8^{16}O$. The mass of the isotope is $16.0amu$.

Q. Helium has a mass number $4$ and the atomic number $2$. Calculate the nuclear binding energy per nucleon. (mass of neutron $=1.00893amu$ and proton $=1.00814amu$, $He=4.0039amu$ and mass of electron is negligible).

Q.

The highest binding energy per nucleon will be for

1. $H_2$
2. $O_2$
3. U
4. Fe

Q.

The highest binding energy per nucleon will be for

1. Fe
2. $H_2$
3. $O_2$
4. U

Q. Nuclear binding energy is the energy released during the hypothetical formation of the nucleus by the condensation of individual nucleons. Thus, binding energy per nucleon =$\frac{\text{Total binding energy}}{\text{Number of nucleons}}$ For example, the mass of hydrogen atom is equal to the sum of the masses of a proton and an electron. For other atoms, the atomic mass is less than the sum of the masses of protons, neutrons and electrons present. This difference in mass, termed as mass defect, is a measure of the binding energy of protons and neutrons in the nucleus. The mass-energy relationship postulated by Einstein is expressed as: $\Delta E=\Delta m{c}^2$
Where $\Delta E$ is the energy liberated, $\Delta m$ is the loss of mass, and c is the speed of light.
In the reaction ${}_1^{2}H{+}_1^{3}H{\to }_2^{4}He{+}_0^{1}n$, if binding energies ${}_1^{2}H{,}_1^{3}H\text{and}{}_2^{4}He$ are respectively a, b and c (in MeV), then the energy released in this reaction is:

1. $a+b+c$
2. $a+b-c$
3. $c-a-b$
4. $c+a-b$

Q. Nuclear binding energy is the energy released during the hypothetical formation of the nucleus by the condensation of individual nucleons. Thus, binding energy per nucleon =$\frac{\text{Total binding energy}}{\text{Number of nucleons}}$ For example, the mass of hydrogen atom is equal to the sum of the masses of a proton and an electron. For other atoms, the atomic mass is less than the sum of the masses of protons, neutrons and electrons present. This difference in mass, termed as mass defect, is a measure of the binding energy of protons and neutrons in the nucleus. The mass-energy relationship postulated by Einstein is expressed as:
$\Delta E=\Delta m{c}^2$
Where $\Delta E$ is the energy liberated, $\Delta m$ is the loss of mass, and c is the speed of light.

$MP$ and $Mn$ are masses of a proton and a neutron respectively. For a nucleus, its binding energy is $B$ and it contains $Z$ protons and $N$ neutrons, the correct relation for this nucleus if $C$ is velocity of light is:

1. $M(N,Z)=N{M}_n+Z{M}_p-B{C}^2$
2. $M(N,Z)=N{M}_n+Z{M}_p+B{C}^2$
3. $M(N,Z)=N{M}_n+Z{M}_p-\frac{B}{C^2}$
   
4. $M(N,Z)=N{M}_n+Z{M}_p+\frac{B}{C^2}$

Q. The binding energy of an element is 64 MeV. If the binding energy per nucleon is 6.4 MeV, then the number of nucleons are 10.

1. True
2. False

Q. If the amount of a radioactive substance is increased three times, the number of atoms disintegrating per unit time would:

1. be double
2. not be change
3. be triple
4. be $\frac{1}{3}$rd of the original number of atoms

Q. At what temperature will the molar kinetic energy of 0.3 mol of helium be the same as that of 0.4 mol of argon at 400 K?

1. 700 K
2. 533 K
3. 800 K
4. 400 K

Q. Assertion :Helium shows only positive deviations from ideal behaviour. Reason: Helium is an inert gas.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect but Reason is correct

Q. The binding energy of ${}_2^{4}He$ is $28.57$ $MeV$. What shall be the binding energy per nucleon of this element?

Q. Nuclear binding energy is the energy released during the hypothetical formation of the nucleus by the condensation of individual nucleons. Thus, binding energy per nucleon =$\frac{\text{Total binding energy}}{\text{Number of nucleons}}$ For example, the mass of hydrogen atom is equal to the sum of the masses of a proton and an electron. For other atoms, the atomic mass is less than the sum of the masses of protons, neutrons and electrons present. This difference in mass, termed as mass defect, is a measure of the binding energy of protons and neutrons in the nucleus. The mass-energy relationship postulated by Einstein is expressed as:
$\Delta E=\Delta m{c}^2$
Where $\Delta E$ is the energy liberated, $\Delta m$ is the loss of mass, and c is the speed of light.

$MP$ and $Mn$ are masses of a proton and a neutron respectively. For a nucleus, its binding energy is $B$ and it contains $Z$ protons and $N$ neutrons, the correct relation for this nucleus if $C$ is velocity of light is:

1. $M(N,Z)=N{M}_n+Z{M}_p-\frac{B}{C^2}$
   
2. $M(N,Z)=N{M}_n+Z{M}_p+\frac{B}{C^2}$
3. $M(N,Z)=N{M}_n+Z{M}_p+B{C}^2$
4. $M(N,Z)=N{M}_n+Z{M}_p-B{C}^2$

Q. Pick out the correct statements:

1. Nuclei with certain even numbers of protons and of neutrons are the most stable
2. ${}_6^{14}\text{C}$ is stable isotope of carbon
3. Nuclides that lie below the belt of stability are proton rich
4. New elements and isotopes of known elements are made by nucleo synthesis

Q. In the given square $P,Q,R,S$ with atomic number is written are metalloids. About this the 4 statements are given below. Select the correct option of the true statements.
$\left(a\right)$ Element after square $P$ is a non-metal
$\left(b\right)$ Square $R$ represents metalloid
$\left(c\right)$ Element just before square $R$ is a metalloid
$\left(d\right)$ Element just before square $S$ is a non-metal

1. $\left(a\right),\left(b\right)$ and $\left(c\right)$
2. $\left(a\right),\left(b\right)$ and $\left(d\right)$
3. $\left(b\right)$ and $\left(c\right)$
4. $\left(a\right),\left(b\right),\left(c\right)$ and $\left(d\right)$

Q. Which of the following correctly completes this nuclear reaction: ${}_7^{14}N{+}_2^{4}He\to X{+}_1^{1}H$? In the reaction what is $X$?

1. ${}_8^{17}O$
2. ${}_9^{16}O$
3. ${}_8^{17}N$
4. ${}_7^{17}N$
5. ${}_8^{16}O$

Q. Given the following binding energies:
$1.{}_8^{17}O\to 131MeV$
$2.{}_{26}^{56}Fe\to 493MeV$
$3.{}_{92}^{238}U\to 1804MeV$
Compare the binding energies per nucleon $(\Delta =\frac{B}{A})$ of the three nuclei.

1. ${\Delta }_O$>${\Delta }_{Fe}$>${\Delta }_U$
2. ${\Delta }_{Fe}$>${\Delta }_O$>${\Delta }_U$
3. ${\Delta }_U$>${\Delta }_O$>${\Delta }_{Fe}$
4. ${\Delta }_U$>${\Delta }_{Fe}$>${\Delta }_O$