Question

The nuclear mass of 56fe is 55.9207 amu. calculate the binding energy per nucleon for 56fe.

Answer 1

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 2

Answer: The binding energy per nucleon is $1.41\times 10^{-12}J$

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:  $_{26}^{56}\textrm{Fe}$  

Number of protons = 26

Number of neutrons = 56 - 26 = 30  

To calculate the mass defect of the nucleus, we use the equation:

$\Delta m=[(n_p\times m_p)+(n_n\times m_n)-M$

where,

$n_p$ = number of protons = 26  

$m_p$ = mass of one proton  = 1.00728 amu

$n_n$ = number of neutrons  = 30  

$m_n$ = mass of one neutron = 1.00866 amu

M = nuclear mass = 55.9207 amu  

Putting values in above equation, we get:  

$\Delta m=[(26\times 1.00728)+(30\times 1.00866)]-55.9207\\\\\Delta m=0.52838amu$

To calculate the binding energy of the nucleus, we use the equation:

$E=\Delta mc^2\\E=(0.52838u)\times c^2$

$E=(0.52838u)\times (931.5MeV)$    (Conversion factor:  $1u=931.5MeV/c^2$  )

$E=492.2MeV=787.52\times 10^{-13}J$   (Conversion factor: $1MeV=1.6\times 10^{-13}J$  )

Number of nucleons in $_{26}^{56}\textrm{Fe}$ atom = 56

To calculate the binding energy per nucleon, we divide the binding energy by the number of nucleons, we get:  

$\text{Binding energy per nucleon}=\frac{\text{Binding energy}}{\text{Nucleons}}$

$\text{Binding energy per nucleon}=\frac{787.52\times 10^{-13}J}{56}=1.41\times 10^{-12}J$

Hence, the binding energy per nucleon is $1.41\times 10^{-12}J$