Respuesta :
Fe (iron) has 26 protons,30 neutrons and 26 electrons. In order to calculate the binding energy, first you need to find the total mass of all particles in the nucleus:
26 x mass of proton + 30 x mass of neutron ( all in a.m.u.) =
say "m"
Mass defect is m- 55.9207 amu, then convert it into grams and
put in equation E = mc2 to get binding energy of Fe.
Divide it by number of nucleons to get binding energy per nucleon.
Answer: The binding energy per nucleon is [tex]1.41\times 10^{-12}J[/tex]
Explanation:
Nucleons are defined as the sub-atomic particles which are present in the nucleus of an atom. Nucleons are protons and neutrons.
We are given a nucleus having representation: [tex]_{26}^{56}\textrm{Fe}[/tex]
Number of protons = 26
Number of neutrons = 56 - 26 = 30
To calculate the mass defect of the nucleus, we use the equation:
[tex]\Delta m=[(n_p\times m_p)+(n_n\times m_n)-M[/tex]
where,
[tex]n_p[/tex] = number of protons = 26
[tex]m_p[/tex] = mass of one proton = 1.00728 amu
[tex]n_n[/tex] = number of neutrons = 30
[tex]m_n[/tex] = mass of one neutron = 1.00866 amu
M = nuclear mass = 55.9207 amu
Putting values in above equation, we get:
[tex]\Delta m=[(26\times 1.00728)+(30\times 1.00866)]-55.9207\\\\\Delta m=0.52838amu[/tex]
To calculate the binding energy of the nucleus, we use the equation:
[tex]E=\Delta mc^2\\E=(0.52838u)\times c^2[/tex]
[tex]E=(0.52838u)\times (931.5MeV)[/tex] (Conversion factor: [tex]1u=931.5MeV/c^2[/tex] )
[tex]E=492.2MeV=787.52\times 10^{-13}J[/tex] (Conversion factor: [tex]1MeV=1.6\times 10^{-13}J[/tex] )
Number of nucleons in [tex]_{26}^{56}\textrm{Fe}[/tex] atom = 56
To calculate the binding energy per nucleon, we divide the binding energy by the number of nucleons, we get:
[tex]\text{Binding energy per nucleon}=\frac{\text{Binding energy}}{\text{Nucleons}}[/tex]
[tex]\text{Binding energy per nucleon}=\frac{787.52\times 10^{-13}J}{56}=1.41\times 10^{-12}J[/tex]
Hence, the binding energy per nucleon is [tex]1.41\times 10^{-12}J[/tex]
