Nuclear Physics

Step 1: Understanding the relation between nuclear radius and mass number.
The relation fm implies that the nuclear radius increases with the cube root of the mass number . This formula is often used to estimate the size of nuclei. The radius depends on the mass number but is not significantly affected by it for large nuclei.

Step 2: Analyzing the options.
(A) The central density of nuclei is independent of : Correct. Since the volume of a nucleus increases with and the mass number is proportional to the volume, the central density of nuclei remains constant as increases.
(B) The volume energy per nucleon is a constant: Incorrect. The volume energy per nucleon does not remain constant and depends on various factors, including the nuclear force and surface effects.
(C) The attractive part of the nuclear force has a long range: Incorrect. The nuclear force is short-range, typically acting only over distances of a few femtometers.
(D) The nuclear force is charge dependent: Incorrect. The nuclear force is mostly charge-independent, although electromagnetic effects can cause minor variations.

Step 3: Conclusion.
The correct answer is (A) because the central density of nuclei remains roughly the same as increases.

Step 1: Understanding the fission process.
In the thermal neutron induced fission of , the fission fragments exhibit a characteristic distribution of yields across different mass numbers. This distribution is typically bimodal, with two peaks corresponding to symmetric and asymmetric fission products.

Step 2: Identifying the correct graph.
The graph corresponding to the distribution of fission fragments usually shows two peaks, one around a mass number of 95 and the other around 135, representing the most common fission products. This is best represented by option (C), where two clear peaks are visible.

Step 3: Conclusion.
Thus, the correct answer is (C), as it best fits the typical yield distribution in fission reactions.