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Zorluk: OrtaMass Defect and Binding Energy

A nucleus contains 66 protons and 66 neutrons. Given that the mass of a proton is 1.0078 u1.0078\text{ u}, the mass of a neutron is 1.0087 u1.0087\text{ u}, and the total binding energy of the nucleus is 93.10 MeV93.10\text{ MeV}, what is the mass of the nucleus in atomic mass units (u\text{u})? (Take 1 u=931 MeV1\text{ u} = 931\text{ MeV})

Cevap: 11.999 u

Cevap

The mass of the nucleus is 11.9990 u11.9990\text{ u}.
To find the mass of the nucleus, first calculate the combined mass of the 6 free protons and 6 free neutrons: 6(1.0078 u)+6(1.0087 u)=12.0990 u6(1.0078\text{ u}) + 6(1.0087\text{ u}) = 12.0990\text{ u}. Next, determine the mass defect from the binding energy: Δm=93.10 MeV931 MeV/u=0.1000 u\Delta m = \frac{93.10\text{ MeV}}{931\text{ MeV/u}} = 0.1000\text{ u}. Finally, subtract the mass defect from the total mass of individual nucleons to get the nuclear mass: 12.0990 u−0.1000 u=11.9990 u12.0990\text{ u} - 0.1000\text{ u} = 11.9990\text{ u}.

Adım Adım Çözüm

1
Calculate the total mass of the individual free protons and neutrons.
Total mass of nucleons = 6(1.0078 u)+6(1.0087 u)=12.0990 u6(1.0078\text{ u}) + 6(1.0087\text{ u}) = 12.0990\text{ u}.
The mass of the constituent particles before binding is the sum of their individual rest masses.
2
Calculate the mass defect from the given binding energy.
Mass defect Δm=93.10 MeV931 MeV/u=0.1000 u\Delta m = \frac{93.10\text{ MeV}}{931\text{ MeV/u}} = 0.1000\text{ u}.
Binding energy and mass defect are related by Eb=Δm×931 MeV/uE_b = \Delta m \times 931\text{ MeV/u}.
3
Subtract the mass defect from the total nucleon mass to obtain the nuclear mass.
Mass of nucleus = 12.0990 u−0.1000 u=11.9990 u12.0990\text{ u} - 0.1000\text{ u} = 11.9990\text{ u}.
Mass defect represents the mass lost when nucleons bind together into a nucleus.

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