How to find binding energy per nucleon

How to find binding energy per nucleon

 Before we start to calculate the binding energy of nuclei, let us look into what binding energy is all about.

 Binding energy is the energy  needed  to hold the aggregate number of protons and neutrons together n a nucleus of an atom, he energy required to split a given nucleus into its constituent protons and neutrons is the binding energy of that nuclei.

In a nucleus of all atoms (except hydrogen with only proton) there are protons and neutrons, theses protons and neutrons are called the nucleons. When we talk of binding energy per nucleon, we refer to the total binding energy of an atom divided by the number of protons and neutrons which equal to the atomic mass of the atom. Therefore to find the binding energy per nucleon of any atom or nucleus we first calculate the total binding energy of the atom, and then divide it by the atomic mass of the atom.

How To Calculate The Actual Mass

 To calculate the binding energy per nucleon of an atom we subtract the measured atomic mass of the said atom from the  actual  atomic mass and use the Einstein mass energy relation of e =mc² to calculate the binding energy.

 The measured atomic mass is the mass obtained from the atoms are actually measured, this mass are mostly  available in periodic table of element as a scientific standard,  the actual mass is the mass obtained  when the individual mass of the protons and neutrons in an atom are calculated.

 To obtain the actual mass for any atom we can use the formula below.

 P(1.007825) + N(1.008665)= actual mass.

 Where P is the number of protons and N is the number of neutrons.

 To find  the number of neutrons

 we subtract the atomic mass from the atomic number

N= A-Z

 where A is the atomic mass and Z is the atomic number or number of protons.

After obtaining our measured mass and actual mass we can find the mass defects, mass defects is the difference between the measured mass and the actual mass.

Calculating The Binding Energy

 let M_P be the mass of  proton and M_N be the mass of neutron

Z is the atomic number and A is the atomic mass.

 the mass defect will therefore be

∆M= Z M_P + (A-Z) M_N

 To calculate the binding energy we use the Einstein mass energy relation,

E =MC²

E is the energy in evolt, and  is the speed of light, given as 3x 10⁸  m/s

E =∆MC²

B =∆MC²

To obtain the binding energy per nucleon we divide value B with A,

i.e  B/A is the binding energy per nucleon.

the average binding energy is 8.4MeV for must nucleis.