What is the approximate radius of the 238U nucleus? Express your answer to two significant figures. How do you find r0?

The approximate radius of a 238U nucleus is about 7.1 femtometers (fm).

To determine the radius of a nucleus, we typically use the formula:

r = r₀ A^1/3

where:

• r = radius of the nucleus
• A = mass number of the nucleus (for 238U, A = 238)
• r₀ = a constant (approximately 1.2 to 1.3 fm)

For 238U, we can use r₀ = 1.2 fm:

r = 1.2 fm * (238)^1/3 ≈ 7.1 fm

This simple model allows us to estimate nuclear sizes and illustrates the relationship between size and the total number of nucleons in the nucleus.