Unlocking Binding Energy Solutions for Part C)ii - Tips and Strategies

In summary, the conversation was about completing part c)ii and d)ii of a question. The person had some trouble with their calculations, but eventually figured out the correct answer. They also discussed finding the volume per atom for a specific element and how to track units in calculations.
  • #1
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Homework Statement
Working out how to calculate binding energy
Relevant Equations
l = 1/2Nne
Here is the question:

Screenshot 2019-12-17 at 13.31.27.png

Stuck on how to complete part c)ii

Here is what I have done so far as well as trying to answer part c)ii

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Any help would be appreciated! Thanks
 
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  • #2
37 kJ = 37x103 J.
 
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  • #3
kuruman said:
37 kJ = 37x103 J.

Oh shoot yes you’re right. I don’t know why I processed it at as mega joules

So doing the following calculation again gives

Binding energy = (2 * 293000) / (6x10^23 * 7) = 1.41x10^-19 J which is closer to the answer but still not right
 
  • #4
296 kJ/kg. You need kJ/mol.
 
  • #5
mjc123 said:
296 kJ/kg. You need kJ/mol.

So to convert from kJ/kg to kJ/mol, I must multiply kJ/kg by the molar mass?

I did this and got the following

Binding energy = 2(293000 * 0.20)/(6x10^23)(7) = 2.79... x10^-20 J which is roughly equal to 2.8x10^-20 J

I also got another part that I need help with if you don’t mind

Not entirely sure how to approach part d)ii but I suppose I had done part d) i right
 

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  • #6
di is right. Not sure what the problem is for dii - find the volume per atom, as you did for Hg.
 
  • #7
mjc123 said:
di is right. Not sure what the problem is for dii - find the volume per atom, as you did for Hg.

To find volume per atom. I know that 1.0691... x10^-4 moles of Hg is contained in 2x10^-4 m^3.

So to firstly get the volume per mole of Hg, I do ' 2x10^-4 / 1.0691...x10^-4 ' which gives 1.870... volume per mole

Dividing 1.870... by avogrado's constant is '1.870... / 6.022x10^23 = 3.106... x 10^-24 volume per atom
Cube rooting volume per atom number should give the spacing which comes out to be '1.459... x10^-8 m'

Would you agree that these steps are the right way of doing this?
 
  • #8
Yes, except that you're talking about neon, not mercury.
 
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  • #9
mjc123 said:
Yes, except that you're talking about neon, not mercury.

Yes, sorry I got mixed up with the wording somehow
 
  • #10
The other thing is that I would be more explicit about tracking units through the calculation. So rather than say "1.870 volume per mole" I would say "1.870 m3 volume per mole"; likewise "3.106 x 10-24 m3 volume per atom". In this case, as you're dealing in m all the time, it's not so critical, but if you're switching between e.g. m and cm, or J and kJ, you can easily make mistakes if you don't keep track of units.
 
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1. What is binding energy?

Binding energy is the minimum amount of energy required to separate a nucleus or particle into its individual components. It is the energy that holds the components together.

2. How is binding energy calculated?

Binding energy is calculated by taking the mass defect, which is the difference between the mass of the nucleus and the sum of the masses of its individual components, and multiplying it by the speed of light squared (E=mc²).

3. What is the significance of binding energy?

Binding energy is significant because it is responsible for the stability of atomic nuclei and the formation of chemical bonds. It also plays a crucial role in nuclear reactions and the release of energy, such as in nuclear power plants or nuclear weapons.

4. How does binding energy affect nuclear stability?

Generally, higher binding energy results in greater nuclear stability. This is because the strong nuclear force, which is responsible for holding the nucleus together, is strongest when the nucleus is tightly bound. Unstable nuclei may undergo radioactive decay in order to become more stable and decrease their binding energy.

5. Can binding energy be created or destroyed?

No, binding energy cannot be created or destroyed. It can only be converted into other forms of energy, such as kinetic energy or thermal energy. This is because of the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted.

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