What is the Binding Energy of Carbon 12?

Click For Summary
SUMMARY

The binding energy of Carbon-12 (12C) can be calculated using the mass decrement formula, where σ (mass decrement) equals W (mass of constituent particles) minus M (actual mass of the atom). For 12C, W is derived from 6 protons, 6 neutrons, and 6 electrons. The mass of a proton is 1.007276 amu, and the mass of an electron is 0.00054858 amu, leading to a total mass of 1.00782 amu for 6 protons and electrons, which does not match the given atomic mass of 1.00794 amu. This discrepancy indicates that the problem provided the relative atomic mass instead of the atomic mass of the hydrogen isotope.

PREREQUISITES
  • Understanding of atomic mass units (amu)
  • Familiarity with the concept of binding energy
  • Knowledge of the mass of subatomic particles (protons, neutrons, electrons)
  • Basic grasp of nuclear physics equations, specifically E=σ*c²
NEXT STEPS
  • Research the calculation of binding energy for different isotopes using mass decrement
  • Explore the differences between atomic mass and relative atomic mass
  • Learn about the isotopes of hydrogen: protium, deuterium, and tritium
  • Study the implications of mass-energy equivalence in nuclear reactions
USEFUL FOR

Students in nuclear physics, educators teaching atomic structure, and anyone interested in the calculations related to binding energy and atomic mass discrepancies.

Typhon4ever
Messages
51
Reaction score
0

Homework Statement



Given that the mass of 1 H is 1.00794 amu, the mass of a neutron is 1.00865 amu and
that the energy equivalent of 1 atomic mass unit (AMU) is 931.5 MeV, what is the
binding energy of 12C (atomic mass = 12.00000 amu)?

Homework Equations



(σ) mass decrement=(W) mass of constituent particles (aka for helium 4 its 4p+4n+4e) - (M) actual mass of atom

E=σ*c^2

The Attempt at a Solution



I want to find the binding energy of carbon 12. So it's σ=W-12. W is 6p+6n+6e. I know the mass of n. But I do not know the mass of p and e.

I am told that 1H=1.00794 amu. So 1.00794=1p+1e-σ. I don't see how this helps me get values for p and e. Help?
 
Physics news on Phys.org
What is the Hydrogen atom ?

ehild
 
ehild said:
What is the Hydrogen atom ?

ehild

A hydrogen atom is one proton and one electron if I remember correctly. Am I supposed to derive the mass of p and e from this?
 
You need only the mass of 6p + 6e=6(p+e). The proton and electron do not merge in the hydrogen atom, they are relatively far away, you can take the mass of the hydrogen atom equal to the mass of the proton + mass of the electron.

ehild
 
Last edited:
ehild said:
You need only the mass of 6p + 6e=6(p+e). The proton and electron do not merge in the hydrogen atom, they are relatively far away, you can take the mass of the hydrogen atom equal to the mass of the proton + mass of the electron.

ehild

Ooh I see. The lack of neutron means I can neglect binding energies. That makes much more sense thank you.
 
Hmm, I just checked the given values of the mass of a proton and electron from the book I have (where the question is from) and I notice that the given mass of the 1 H and what can be added from the following data does not add up.

proton: 1.007276 u
electron: 0.00054858 u
p+e=1.00782 which does not = 1.00794

:\
 
There is some confusion between the atomic mass and the relative atomic mass The atomic mass or relative isotopic mass refers to the mass of a single particle, and is fundamentally different from the quantities elemental atomic weight (also called "relative atomic mass") and standard atomic weight, both of which refer to averages (mathematical means) of naturally-occurring atomic mass values for samples of elements
http://en.wikipedia.org/wiki/Atomic_mass

The hydrogen element occurs as mixture of hydrogen, deuterium and tritium isotopes, its relative atomic mass is 1.00794 ± 0.00001 u.
The hydrogen isotope, which consist of a single proton and a single electron, has atomic mass of 1.00782505 u.


So the problem gave a wrong value ...the relative atomic mass of the element instead of the atomic mass of the hydrogen isotope.

ehild
 
Last edited:

Similar threads

  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
Replies
9
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
6K