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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?

1. 2^(1/3): 1
2. 3^(1/2): 1
3. 3^(1/2): 1
4. 2: 1

Correct answer: 2^(1/3): 1

Solution

Momentum conservation gives m1*v1 = m2*v2, so with v1:v2 = 2:1 the masses are m1:m2 = 1:2. Since mass ~ R^3, the radii are in ratio (1:2)^(1/3), i.e. the larger-to-smaller radius ratio is 2^(1/3) : 1.

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