To verify a statement:
From Section 21.6 of the textbook read this statement - “no energy would be released if two
Verify this statement by calculating the binding energy of
Answer to Problem 21.109QA
Solution:
Binding energy for
Binding energy for 2 atoms of
The binding energies of
Explanation of Solution
1) Concept:
To calculate the binding energy of the nuclei of two isotopes, we need to calculate the mass defect of the nuclei. From the exact mass of the isotopes, we will calculate the exact mass of each isotope. From the mass of each isotope, we will calculate the mass of the nucleons. Calculate the mass of the nucleus by using the mass of photons and neutrons. Calculate the mass defect from the mass of nucleus and mass of nucleons. We will calculate the binding energy from mass defect.
2) Formula:
i)
ii)
3) Given:
i) Mass of
ii) Mass of
iii) Mass of single neutron is
iv) Mass of single proton is
v) Mass of electrons is
4) Calculations:
First we convert the exact mass of one atom of each isotope from
Since we are comparing the masses of
Next we calculate the mass of the protons and neutrons in the nucleus of one atom of each isotope:
The difference between the exact mass of the nucleus of the isotope and its subatomic particles is
Calculation of the binding energy corresponding to this difference in mass:
It is the binding energy of just a single helium nucleus. The binding energy for two helium nuclei is
The binding energies of
Conclusion:
We calculated the binding energy of each isotope from the exact mass and mass defect.
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Chapter 21 Solutions
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