Question

Find the radius of a ( ²³⁸{Pu} ) nucleus, a manufactured nuclide used as a power source on some space probes.

a) (2.34 times 10⁻¹⁵) m
b) (3.89 times 10⁻¹⁵) m
c) (6.02 times 10⁻¹⁶) m
d) (9.21 times 10⁻¹⁶) m

Answer 1

The radius of the Plutonium-238 nucleus can be calculated using the formula r = r_{0}A^{1/3}, where r_{0} is 1.2 x 10^-15 meters and A is 238 for Pu-238.

Step-by-step explanation:

The radius of a nucleus can be estimated using the empirical formula r = r_{0}A^{1/3}, where r_{0} is a constant approximately equal to 1.2 x 10-15 meters and A is the mass number of the nuclide. Considering Plutonium-238 (²³⁸Pu) is the nuclide in question with a mass number of 238, the calculation for its radius would be:

r = (1.2 x 10-15 m) x (238)1/3

By calculating this, we can find the approximate radius of the Plutonium-238 nucleus.

The options provided in this context are approximate values. Therefore, a student should perform the calculation to find which of these options is closest to the result obtained from using the formula.