alleryStart learning →The nucleus of fluorine-18 has a mass defect of 2.44 x 10^-28 kg. Using c = 3.00 x 10^8 m/s, what is its binding energy?
A7.3 x 10^-20 J
B2.2 x 10^-20 J
C2.2 x 10^-11 J
D2.4 x 10^-28 J
Answer & Solution
Correct answer: C. 2.2 x 10^-11 J
1. Binding energy equals the mass defect multiplied by c squared: E0 = m c^2.
2. Substitute m = 2.44 x 10^-28 kg and c = 3.00 x 10^8 m/s.
3. Square the speed of light: (3.00 x 10^8)^2 = 9.00 x 10^16.
4. Multiply: E0 = (2.44 x 10^-28)(9.00 x 10^16) = 2.2 x 10^-11 J.
5. 2.4 x 10^-28 J simply repeats the mass value without converting it, and 2.2 x 10^-20 J and 7.3 x 10^-20 J do not match this multiplication.
6. So 2.2 x 10^-11 J is correct.
_Source: OpenStax Physics (CC BY 4.0), Ch 10 "Special Relativity", section 10.2 Consequences of Special Relativity_
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