For a nucleus AAX having mass number A and atomic number Z
A. The surface energy per nucleon \((b_s)=−a_1A^{\frac{2}{3}} \)
B. The Coulomb contribution to the binding energy \(b_c=−a_2\frac{Z(Z−1)}{A^{\frac{4}{3}}} \)
C. The volume energy b_v=a₃A
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. ( a₁,a₂ and a₃ are constants)
Choose the most appropriate answer from the options given below:

Question

A soap bubble of surface tension \(0.04\,\text{N/m}\) is blown to a diameter of \(7\,\text{cm}\). If \((15000 - x)\,\mu\text{J}\) of work is done in blowing it further to make its diameter \(14\,\text{cm}\) \((\pi = 22/7)\), then the value of \(x\) is ________.

Answer 1

To determine the most appropriate answer, let's evaluate each statement given in the question.

Statement A: The surface energy per nucleon \((b_s)=-a_1A^{\frac{2}{3}}\)
This statement describes the surface energy term in terms of the mass number \(A\). The surface energy for a nucleus typically depends on \(A^{\frac{2}{3}}\) to account for the surface area, which suggests it's conceptually correct. However, since the question is about selecting a combination of valid statements, we'll check others to see if this is relevant to the final choice.
Statement B: The Coulomb contribution to the binding energy \(b_c=-a_2\frac{Z(Z−1)}{A^{\frac{4}{3}}}\)
This represents the repulsion between protons within the nucleus. It is a part of the semi-empirical mass formula and provides an explanation for the decrease in binding energy due to electrostatic repulsion. This statement is valid.
Statement C: The volume energy \(b_v = a_3A\)
This represents the volume energy term, which is proportional to the number of nucleons \(A\). This is standard in the liquid drop model, where volume energy is directly proportional to \(A\). This statement is valid and commonly accepted in nuclear physics.
Statement D: Decrease in the binding energy is proportional to surface area.
The surface energy term implies that the stability decreases as the surface area increases, which means a larger nucleus with more surface area is less tightly bound proportionally. This is a correct statement.
Statement E: While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons.
While this statement seems reasonable from a geometrical packing standpoint, it is not part of the semi-empirical mass formula elements discussed broadly in such questions; typically, coordination number doesn't explicitly feature in statements about energy contributions. Therefore, this statement isn't always correct within this context.

Considering all of the statements, the most appropriate answer would be C, D only, since these two statements (volume energy related and surface area dependency) align with the principles found in nuclear physics, specifically in the context of the binding energy and surface effects.

Answer 2

To determine the most appropriate answer, let's evaluate each statement given in the question.

Statement A: The surface energy per nucleon \((b_s)=-a_1A^{\frac{2}{3}}\)
This statement describes the surface energy term in terms of the mass number \(A\). The surface energy for a nucleus typically depends on \(A^{\frac{2}{3}}\) to account for the surface area, which suggests it's conceptually correct. However, since the question is about selecting a combination of valid statements, we'll check others to see if this is relevant to the final choice.
Statement B: The Coulomb contribution to the binding energy \(b_c=-a_2\frac{Z(Z−1)}{A^{\frac{4}{3}}}\)
This represents the repulsion between protons within the nucleus. It is a part of the semi-empirical mass formula and provides an explanation for the decrease in binding energy due to electrostatic repulsion. This statement is valid.
Statement C: The volume energy \(b_v = a_3A\)
This represents the volume energy term, which is proportional to the number of nucleons \(A\). This is standard in the liquid drop model, where volume energy is directly proportional to \(A\). This statement is valid and commonly accepted in nuclear physics.
Statement D: Decrease in the binding energy is proportional to surface area.
The surface energy term implies that the stability decreases as the surface area increases, which means a larger nucleus with more surface area is less tightly bound proportionally. This is a correct statement.
Statement E: While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons.
While this statement seems reasonable from a geometrical packing standpoint, it is not part of the semi-empirical mass formula elements discussed broadly in such questions; typically, coordination number doesn't explicitly feature in statements about energy contributions. Therefore, this statement isn't always correct within this context.

Considering all of the statements, the most appropriate answer would be C, D only, since these two statements (volume energy related and surface area dependency) align with the principles found in nuclear physics, specifically in the context of the binding energy and surface effects.

Show Hint

The Correct Option is C

Solution and Explanation

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