Mass Defect: Pb-210 Nuclear Binding Energy

In summary, Mass Defect is the difference in mass between an atom and the sum of its subatomic particles. It is directly related to the energy released in radioactive decay, such as in Pb-210 Nuclear Binding Energy. Mass Defect is measured in atomic mass units or kilograms, and its significance lies in its role in nuclear reactions, including powering nuclear reactors and atomic bombs. While Mass Defect does not directly affect the stability of an atom, it is a byproduct of the strong nuclear force and is lower in more stable atoms. Finally, Mass Defect can be used to determine the energy released in a nuclear reaction by calculating the difference in mass and converting it into energy units.
  • #1
MrDMD83
25
0

Homework Statement



For lead N=210 Z=82 Pb (atomic mass = 209.984163 u) obtain each of the following:
(a) The mass defect in atomic mass units
u
(b) the binding energy (in MeV)
MeV
(c) the binding energy per nucleon (in MeV)
MeV


Homework Equations





The Attempt at a Solution



a) 82 x 1.6726e-27 kg + 128 x 1.6749e-27 kg= 3.515e-25 kg

3.515e-25kg x 1u/1.6605e-27= 211.708

211.708-209.984163= 1.72u but it says my answer is wrong.
 
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  • #2
Nevermind. I forgot to initially subtract the mass of the 82 electrons from the mass of entire atom.
 
  • #3
Can you explain why?

b) E=mc^2

= 3.515e-25 kg x (3.00e8 m/s)^2

= 3.16e-8 J

1 J= 6.24e18 MeV

3.16e-8 J x 6.24e18 MeV/1 J= 1.97e11 MeV

c) 1.97e11 MeV/210 nucleons= 9.38e8 MeV per nucleon

The mass defect is correct, but the binding energy and binding energy per nucleon seem to be incorrect. The binding energy should be the difference between the mass of the nucleus and the sum of the masses of its individual protons and neutrons. In this case, it would be the difference between 209.984163u and 211.708u, which is -1.724u. To convert this to MeV, we use the conversion factor 931.5 MeV/u, giving us a binding energy of -1.603 MeV.

For the binding energy per nucleon, we divide the binding energy by the number of nucleons, which in this case is 210. This gives us a value of -0.0076 MeV per nucleon. Note that the negative sign indicates that energy is released when the nucleus is formed, as the mass of the nucleus is less than the sum of its individual particles.
 

1. What is Mass Defect and how does it relate to Pb-210 Nuclear Binding Energy?

Mass Defect is the difference between the mass of an atom and the sum of the masses of its individual subatomic particles. Pb-210 Nuclear Binding Energy refers to the energy released when Pb-210 atoms undergo radioactive decay. Mass Defect is directly related to this energy release, as the difference in mass is converted into energy according to Einstein's famous equation, E=mc^2.

2. How is Mass Defect measured?

Mass Defect is measured in atomic mass units (amu) or in kilograms (kg). The mass of an atom is measured by comparing it to the mass of a carbon-12 atom, which is defined as exactly 12 amu. The difference in mass between an atom and the sum of its subatomic particles is then calculated and converted into energy units.

3. What is the significance of Mass Defect and Pb-210 Nuclear Binding Energy?

The significance of Mass Defect and Pb-210 Nuclear Binding Energy lies in their role in nuclear reactions. The energy released from Mass Defect is what powers nuclear reactors and atomic bombs. Pb-210 Nuclear Binding Energy is specifically important because it is a common isotope used in cancer treatments and in the production of radon gas for industrial purposes.

4. How does Mass Defect affect the stability of an atom?

Mass Defect does not directly affect the stability of an atom. However, it is a byproduct of the strong nuclear force, which is the force that holds the nucleus together. The more stable an atom is, the lower its Mass Defect will be. This is because the strong nuclear force is stronger than the electromagnetic repulsion between protons, resulting in a smaller Mass Defect.

5. Can Mass Defect be used to determine the energy released in a nuclear reaction?

Yes, Mass Defect can be used to determine the energy released in a nuclear reaction. By measuring the difference in mass between the reactants and products of a reaction, Mass Defect can be calculated and converted into energy units. This allows scientists to accurately predict and control the energy released in nuclear reactions.

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