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A nucleus splits into two fragments, and the speeds of the fragments are in the ratio 2:1. What is the ratio of their nuclear radii?
- 3^(2/3): 1
- 1: 2^(1/3)
- 2^(1/3): 1
- 1: 3^(2/3)
Correct answer: 1: 2^(1/3)
Solution
The ratio of the speeds of the fragments is inversely related to the square root of their masses due to conservation of momentum. Given the speed ratio of 2:1, the mass ratio becomes 1:4. Since the nuclear radius is proportional to the cube root of the mass, the ratio of their radii is 1:2^(1/3).
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