Final answer:
The mass number A of a nucleus with a radius of 4.8 femtometers is determined using the formula r = ro A^(1/3) with ro = 1.2 fm. After solving the equation, the result is A = 64.
Step-by-step explanation:
To find the mass number A when the radius r of the nucleus equals 4.8 femtometers (fm), we use the formula r = ro A1/3, where ro equals 1.2 fm, which is the approximate radius of a single proton. We are given that r is 4.8 fm, so plugging these values into the equation, we have:
4.8 fm = (1.2 fm) A1/3
To solve for A, we first divide both sides by 1.2 fm to isolate A to the power of one-third:
(4.8 fm) / (1.2 fm) = A1/3
4 = A1/3
To find A, we need to raise both sides of the equation to the power of three:
(A1/3)3 = 43
A = 64
The mass number A is therefore 64.