What is the approximate nuclear radius r of the isotope 208 82Pb (lead-208)?

• A. 0.53 \, \text{Å}
• B. 208 \, \text{fm}
• C. 7.1 \, \text{fm}
• D. 1.2 \, \text{fm}

Answer: (C)

Verified step by step guidance

1. Recall that the nuclear radius \(r\) of an isotope can be estimated using the empirical formula: \[r = r_0 \times A^{1/3}\] where \(r_0\) is a constant approximately equal to 1.2 fm (femtometers), and \(A\) is the mass number (total number of protons and neutrons).
2. Identify the mass number \(A\) for the isotope \(^{208}_{82}\text{Pb}\). Here, \(A = 208\).
3. Substitute the values into the formula: \[r = 1.2 \, \text{fm} \times (208)^{1/3}\]
4. Calculate the cube root of 208, which represents how the radius scales with the size of the nucleus.
5. Multiply the constant \(r_0\) by the cube root of 208 to find the approximate nuclear radius \(r\) in femtometers.