The mass of carbon-12 is $\pu{12 u}$ by definition. However, one carbon-12 atom comprises 6 neutrons (each weighing $\pu{1.0087 u}$), 6 protons (each weighing $\pu{1.0072 u}$), and 6 electrons (each weighing $\pu{0.0005 u}$), which all add up to $\pu{12.0894 u}$.
Where does the $0.7\%$ difference in mass come from?
Answer
This is due to the mass-energy equivalence and a phenomenon called binding energy.
Forming a nucleus releases energy because the nucleons are falling into a potential energy well. Due to Einstein's mass energy equivalence this results in the mass of the new nucleus being less than that of the particles that formed it.
The binding energy of carbon-12 is quoted on Wikipedia as $\pu{92.162 MeV}$. Therefore we can estimate the mass defect of a carbon-12 atom, $\Delta m$, using $ E = (\Delta m)c^2$:
$$\Delta m = \frac{(\pu{92.162 \times 10^6 eV})(\pu{1.6022 \times 10^-19 J eV-1})}{(\pu{2.9979 \times 10^8 m s-1})^2} = \pu{1.6430 \times 10^-28 kg} = \pu{0.098943 u}$$
The difference in the mass of carbon-12 to the mass of its constituent particles is $\pu{0.08940 u}$, so we can see that our calculation is a reasonable estimate of the mass defect. The slight difference is due to other more complicated factors that I have not taken into account, but it still illustrates the main reason for the mass defect.
No comments:
Post a Comment