Mass Defect & Binding Energy

2 Marks Questions

1. Using the curve for the binding energy per nucleon as a function of mass number A, state

clearly how the release in energy in the processes of nuclear fission and nuclear fusion can be explained. [All India 2011]

Ans.

The binding energy per nucleon curve is shown as below:

MeV ⁵⁶Fe Most stable nuclei 8 238_U

Binding energy per nucleon 4 Nuclei prone to fusion Nuclei prone to fission

2 <math>^{2}H</math>

0 20 60 100 140 180 220 Mass number A --- Binding energy per nucleon as a function of mass number A (1)

Explanation of Release of Energy in Nuclear Fission and Fusion The curve reveals that binding energy per nucleon is smaller for heavier nuclei than the middle level nuclei. This shows that heavier nuclei are less stable than middle level nuclei. In nuclear fission, binding energy per nucleon of reactants (heavier nuclei) changes from nearly 7.6 MeV to 8.4 MeV (for nuclei of middle level mass). Higher value of the binding energy of the nuclear product results in the liberation of energy during the phenomena of nuclear fission

In nuclear fusion, binding energy per nucleon of lighter nuclei into heavier one changes from low value of binding energy per nucleon to high value and release of energy takes place in fusion e.g., two ₁H² (Binding energy per nucleon = 1.5 MeV/nucleon) combine to form ₂He⁴ (Binding energy per nucleon ≈ 7 MeV/nucleon) and therefore the energy is liberated during nuclear fusion. (1/2)

2.Draw a plot of potential energy of a pair of nucleons as a function of their separation. Write two important conclusions which you can draw regarding the nature of nuclear forces. [All India 2010]

Ans.

Graph manifests that 200 100 puls 0 9 Attraction -100 2 <math>3 \times 10^{-13} \, \text{cm}</math> Graph between the potential energy of a pair of nucleons as a function of (1) The conclusions drawn from the graph are given as below:

1. Nuclear force is a short range force.
2. Nuclear force is of attractive nature when separation between the nuclei greater than 1 fm and of repulsive nature when separation is less than 1 fm. (1)

3.Draw a plot of the binding energy per nucleon as a function of mass number for a large number of nuclei 20 > A > 240. How do you explain the constancy of binding energy per nucleon in the range of 30<A<170 using the property that nuclear force is short-ranged? [All India 2010]

Ans.

The binding energy per nucleon curve is shown as below:

MeV ⁵⁶Fe Most stable nuclei He 8 16O ²³⁸U Binding energy per nucleon 4 Nuclei prone to fusion Nuclei prone to fission

2 <math>^{2}H</math>

0 20 60 100 140 180 220 Mass number A ---- Binding energy per nucleon as a function of mass number A (1)

Explanation of Release of Energy in Nuclear Fission and Fusion The curve reveals that binding energy per nucleon is smaller for heavier nuclei than the middle level nuclei. This shows that heavier nuclei are less stable than middle level nuclei. In nuclear fission, binding energy per nucleon of reactants (heavier nuclei) changes from nearly 7.6 MeV to 8.4 MeV (for nuclei of middle level mass). Higher value of the binding energy of the nuclear product results in the liberation of energy during the phenomena of nuclear fission

In nuclear fusion, binding energy per nucleon of lighter nuclei into heavier one changes from low value of binding energy per nucleon to high value and release of energy takes place in fusion e.g., two ₁H² (Binding energy per nucleon ≈ 1.5 MeV/nucleon) combine to form ₂He⁴ (Binding energy per nucleon <math>\approx</math> 7 MeV/nucleon) and therefore the energy is liberated during nuclear fusion. (1/2)