- #1
Amrator
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This is taken from page 226 in Essential Astrophysics by Lang:
"The mass defect, ##ΔM##, for a nucleus containing ##A## nucleons, ##Z## protons, and ##A-Z## neutrons is
$$ΔM = Z m_p + (A - Z) m_n - m_{nuc}$$ where ##A## is the mass number of the nucleus, ##Z## is the atomic number, ##m_p## is the mass of the proton, ##m_n## is the mass of the neutron, and ##m_{nuc}## is the mass of the nucleus.
The binding energy, ##E_B##, used to assemble the nucleus from its constituent nucleons is:
$$E_B = ΔM c^2$$ The binding energy measures how tightly bound a nucleus is."
So mass defect represents both the difference between the mass of a composite particle and the sum of the masses of its parts and the binding energy released during nuclear fusion? If I wanted to calculate the binding energy released during the proton-proton chain reaction, would I simply plug in 938.272 MeV for ##m_p##, 939.5654 MeV for ##m_n##, 2 for ##Z##, 2 for ##A-Z## (4 total nucleons minus 2 protons for a helium atom), and 3727.379 MeV for ##m_{nuc}##? This gives me 28.2958 MeV. Multiplying that by (3 x 10^8 m/s)^2 gives me 2.54662 x 10^18. Is this correct? Is that the energy released during a nuclear fusion reaction in a main sequence star?
If it helps to know, I took both calculus-based E&M (level of Purcell) and multi-variable calculus/vector calculus last semester. I have not taken university-level chemistry yet.
Thanks, guys!
"The mass defect, ##ΔM##, for a nucleus containing ##A## nucleons, ##Z## protons, and ##A-Z## neutrons is
$$ΔM = Z m_p + (A - Z) m_n - m_{nuc}$$ where ##A## is the mass number of the nucleus, ##Z## is the atomic number, ##m_p## is the mass of the proton, ##m_n## is the mass of the neutron, and ##m_{nuc}## is the mass of the nucleus.
The binding energy, ##E_B##, used to assemble the nucleus from its constituent nucleons is:
$$E_B = ΔM c^2$$ The binding energy measures how tightly bound a nucleus is."
So mass defect represents both the difference between the mass of a composite particle and the sum of the masses of its parts and the binding energy released during nuclear fusion? If I wanted to calculate the binding energy released during the proton-proton chain reaction, would I simply plug in 938.272 MeV for ##m_p##, 939.5654 MeV for ##m_n##, 2 for ##Z##, 2 for ##A-Z## (4 total nucleons minus 2 protons for a helium atom), and 3727.379 MeV for ##m_{nuc}##? This gives me 28.2958 MeV. Multiplying that by (3 x 10^8 m/s)^2 gives me 2.54662 x 10^18. Is this correct? Is that the energy released during a nuclear fusion reaction in a main sequence star?
If it helps to know, I took both calculus-based E&M (level of Purcell) and multi-variable calculus/vector calculus last semester. I have not taken university-level chemistry yet.
Thanks, guys!