Four statements are given (A is mass number) :
A. The volume of a nucleus is proportional to $A^{1/3}$.
B. The volume of a nucleus is proportional to A.
C. The difference in mass of an atom and its nucleus is called the mass defect.
D. The difference in mass of a nucleus and its constituent nucleons is called the mass defect.
Choose the correct answer from the options given below :
Nuclear Statement Analysis
We need to evaluate the truthfulness of four statements related to nuclear properties.
Statement A Analysis
The radius ($R$) of a nucleus is empirically found to be proportional to the cube root of the mass number ($A$): $R \propto A^{1/3}$
The volume ($V$) of a nucleus is proportional to the cube of its radius: $V \propto R^3$
Substituting the relation for $R$: $V \propto (A^{1/3})^3 = A$
Therefore, the volume of a nucleus is proportional to $A$, not $A^{1/3}$. Statement A is false.
Statement B Analysis
As derived above, the volume ($V$) of a nucleus is directly proportional to the mass number ($A$). $V \propto A$
Statement B is true.
Statement C Analysis
The mass defect is specifically defined as the difference between the mass of the individual nucleons (protons and neutrons) and the actual measured mass of the nucleus. The mass of electrons in an atom is generally not included in this specific definition of nuclear mass defect. Therefore, this statement is an inaccurate definition. Statement C is false.
Statement D Analysis
The mass defect ($\Delta m$) is precisely the difference between the total mass of the constituent nucleons (protons and neutrons) and the measured mass of the nucleus. $\Delta m = (\text{Mass of constituent nucleons}) - (\text{Mass of nucleus})$
Statement D provides the correct definition. Statement D is true.
Conclusion
Based on the analysis:
- Statement A is false.
- Statement B is true.
- Statement C is false.
- Statement D is true.
Therefore, statements B and D are true, while A and C are false.
Similar Questions
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$$^{238}\text{U} \rightarrow ^{234}\text{Th} + ^{4}\text{He}$$
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Important Questions from Modern Physics
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The binding energy for the following nuclear reactions are expressed in MeV.
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${}_2\text{He}^4 + {}_0\text{n}^1 \rightarrow {}_2\text{He}^5 - 0.9 \text{ MeV}$
If $\text{X}_3, \text{X}_4, \text{X}_5$ denote the stability of ${}_2\text{He}^3, {}_2\text{He}^4$ and ${}_2\text{He}^5$, respectively, then the correct order is :Identify the correct truth table of the given logic circuit.
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