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An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8: 27. The ratio of the radii of the nuclei (assumed to be spherical) is

1. 8: 27
2. 2: 3
3. 3: 2
4. 4: 9

Correct answer: 3: 2

Solution

The ratio of the velocities of the two nuclei is inversely related to the square root of their masses, and since the masses are proportional to the cube of their radii (for spherical shapes), we can derive the ratio of the radii from the velocity ratio. Thus, if the velocities are in the ratio of 8:27, the ratio of the radii will be the square root of the inverse of that ratio, leading to a ratio of 3:2.

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