Binding energy calculation of a nucleus

In summary, the student is trying to calculate the binding energy of the nucleus of the isotope 11B. They data given is 11B: m = 11,0093 amu (Z = 5) (Z = # of p+ (I assume, since the # of p+ relates to the "iso" part of isotope)). They calculate that mass/proton = 1,007276 amu, mass/neutron = 1,008665 amu, and then assume that the binding energy is ∆m·C2. They try to solve for ∆m and get a value of 0.07907 amu. They then convert this value into MeV and get 4,44E28
  • #1
ellynx
5
0
Hello,

I'd appreciate feedback on my calculation of binding energy, just wanted to check if I'm on the right track w/ regards to calculation steps (and thought process).

I'll try to be as clear as possible, please give me input if there's some notations / steps I should correct and keep in mind I have limited knowledge on the subject.


Homework Statement


Basically I want to calculate the binding energy per nucleus of the isotope 11B in MeV.

Binding energy of the nucleus, which is the energy keeping the protons and neutrons together, thus the energy needed to break apart the "bonds" between the p+'s and n0's.
(in terms of force notation, would this be the strong nuclear force?)


Data given:

11B: m = 11,0093 amu (Z = 5) (Z = # of p+ (I assume, since the # of p+ relates to the "iso" part of isotope))


mass/proton = 1,007276 amu
mass/neutron = 1,008665 amu


Homework Equations



∆m = (sum of protons and neutrons) - (measured mass of the isotope)

E=mC2

binding energy = ∆m·C2

The Attempt at a Solution



11B ∑m = 5p+ * 1,007275 amu + 6n0 * 1,008665 amu = 11,08837 amu (the unbound system calculated mass)

11B m = 11,0093 amu (measured somehow)


∆m = 11,08837 - 11,0093 = 0,07907 amu

Binding energy = 0,07907 amu * (3E8 m/s)^2 = 7,1163E15 J ( is it safe to say this is joules kg·m^2/s^2 ?) or do I need to convert amu's into Kg's first?

Assuming I get the result in J I continue to convert into MeV:

1 J = 6,24E18 eV = 6,24E12 MeV

MeV: 7,1163E15*J * 6,24E12 MeV/J = 4,44E28 MeV

This seems to me like a LOT of energy, how can I best evaluate my answer? Does this amount of energy seem like a reasonable amount? Can I relate it to the strong nuclear force?

Thanks.
 
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  • #2
I looked up some binding energy values, and they all lay in quite a different interval. That value I got has to be horrendously off course.

Maybe I should divide by the atom number, but then again I would still get a pretty crazy value.
 
  • #3
I think you're more likely to get a response to this in the physics sections for homework questions (don't ask me where!). I don't think you can post the same question twice though, you may like to ask a moderator to transfer it, perhaps.
 
  • #4
ellynx said:
do I need to convert amu's into Kg's first?

Yes.

--
 

What is binding energy?

Binding energy is the amount of energy required to break apart a nucleus into its individual component parts, such as protons and neutrons.

Why is calculating binding energy important?

Calculating binding energy allows scientists to better understand the stability and structure of a nucleus, as well as its potential for nuclear reactions.

How is binding energy calculated?

Binding energy is typically calculated using the mass defect of a nucleus, which is the difference between the mass of the nucleus and the sum of the masses of its individual components.

What factors affect the binding energy of a nucleus?

The primary factors that affect binding energy are the number of protons and neutrons in the nucleus, the strong nuclear force that holds the nucleus together, and the electrostatic repulsion between protons.

What are some practical applications of binding energy calculations?

Binding energy calculations are used in fields such as nuclear physics, astrophysics, and nuclear engineering to study nuclear reactions, design nuclear reactors, and understand the formation and evolution of stars and galaxies.

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