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The nuclear radius formula is r = r0 A^(1/3), with r0 = 1.2 femtometres. What is the radius of an aluminum-27 nucleus?
A1.2 fm
B2.4 fm
C3.6 fm
D4.8 fm
Answer & Solution
Correct answer: C. 3.6 fm
1. Apply r = r0 A^(1/3) with r0 = 1.2 fm and A = 27.
2. The cube root of 27 is exactly 3, since 3 cubed equals 27.
3. Multiply: r = 1.2 x 3 = 3.6 fm.
4. 1.2 fm is just r0 itself, without multiplying by the cube root of A.
5. 2.4 fm and 4.8 fm do not match this multiplication.
6. So 3.6 fm is correct.
_Source: OpenStax Physics (CC BY 4.0), Ch 22 "The Atom", section 22.2 Nuclear Forces and Radioactivity_
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