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* 10^(-12)J`

Step-by-step 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* m_p)+(n_n* 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* 1.00728)+(30* 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)* c^2`

`E=(0.52838u)* (931.5MeV)` (Conversion factor:
`1u=931.5MeV/c^2` )

`E=492.2MeV=787.52* 10^(-13)J` (Conversion factor:
`1MeV=1.6* 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}=(787.52* 10^(-13)J)/(56)=1.41* 10^(-12)J`

Hence, the binding energy per nucleon is
`1.41* 10^(-12)J`