# How to calculate the binding energy ???

please explain as if you were explaining it to a kid ??

• The He atom is composed of 2 protons, 2 neutrons and 2 electrons.

The mass of 2 protons = 2 x 1.007277 amu

The mass of 2 neutrons = 2 x 1.008665 amu

The mass of 2 electrons = 2 x 0.0005486 amu

The sum of the masses is 4.032981 amu

The actual mass, as measured by a mass spectrometer, is 4.002603 amu.

The difference (4.032981 – 4.002603) is 0.030378 amu

For one mole of He atoms the difference would be 0.030378 grams

Why is there a difference?

If we were to break apart a He atom into protons, neutrons and electrons, a tremendous amout of evergy would be required. The amount of energy is called the binding energy. Obviously if we were to form a He atom from protons, neutrons, and electrons a tremendous amount of energy would be released. The amount of energy is equal to the binding energy.

Where did the energy come from?

Einstein showed that mass and energy are related by the equation E = mc^2.. Using the speed of light, c, of 2.9979×10^8 m/s and the mass that was lost when the He was formed (3.0378×10^-5 kg) the calculated binding energy is 2.7302×10^12 kg m^2 s^2.

1 joule = 1 kg m^2 s^2 so the binging energy of 1 mol He = 2.73×10^12 J/mol or 2.73×10^9 kJ/mol.

The binding energy is usually expressed in energy units of Mev (1 million electron volts). 931 MeV is approximately equal to the mass of 1 amu. Thus, the mass of 0.030378 amu = 931 x 0.030378 = 28.3 MeV

The binding energy of a He atom is 28.3 MeV

The He atom is composed of 4 nucleons (2 protons + 2 neutrons), so the average binding energy per nucleon is 28.3 MeV/4 = 7.07 MeV. The average bindfing energy per nucleon varies for different atoms.

• Nuclear Binding Energy

• The key concept behind the release of energy in fusion (and fission) reactions is binding energy. Binding energy is the energy that is lost when a nucleus is created from protons and neutrons. If you added up the total mass of the nucleons (protons and neutrons) that compose an atom, you would notice that this sum is less than the actual mass of the atom. This missing mass, called the mass defect, is a measure of the atom’s binding energy. It is released during the formation of a nucleus from the composing nucleons. This energy would have to be put back into the nucleus in order to decompose it into its individual nucleons. The greater the binding energy per nucleon in the atom, the greater the atom’s stability. To calculate the binding energy of a nucleus, all you have to do is sum the mass of the individual nucleons, and then subtract the mass of the atom itself. The mass leftover is then converted into its energy equivalent. The relation between mass and energy is shown in Einstein’s famous equation E = mc2. However, we will just multiply the mass by a conversion factor to have the units of energy in millions of electron volts (MeV), a standard unit of energy in nuclear physics. Therefore, the equation for binding energy that you can use later is:

Eb = (Z × mH + N × mn – misotope) × 931.5 MeV/amu

Eb = binding energy, in MeV

Z = number of protons

mH = mass of a hydrogen atom (1.007825 atomic mass units, or amu)

N = number of neutrons

mn = mass of a neutron (1.008664904 amu)

misotope = actual mass of the isotope

931.5 Mev/amu = the conversion factor to convert mass into energy, in units of MeV.

• I don’t know how you get so much like, Skipper, but In the IB physics Markscheme May 2014 TZ2 Paper 2:

1. you don’t have to include electron when measuring the sum of the masses. Therefore:

Massdifference=Nuclearmass – (Massofprotons*Massofneutrons)

2. You don’t need E=mc^2. Skip directly to:

3. Binding energy = [ 931.5MeV*(Massdifference) ] / (Number of proton)

Simple.

• Binding energy=mass of an unbound atom*c^2- mass of a bound atom*c^2

c=3.0*10^8

for the mass of the unbound atom you need to look up the weight of a hydrogen-1 atom(proton) and a neutron

If you want the answer in MeV just multiply by 931.494, otherwise its in u

• The difference between the mass of a nucleus and the sum of the masses of the nucleons of which it is composed is called the mass defect. Three things need to be known in order to calculate the mass defect:

the actual mass of the nucleus,

the composition of the nucleus (number of protons and of neutrons),

the masses of a proton and of a neutron.

To calculate the mass defect:

add up the masses of each proton and of each neutron that make up the nucleus,

subtract the actual mass of the nucleus from the combined mass of the components to obtain the mass defect.

Example: Find the mass defect of a copper-63 nucleus if the actual mass of a copper-63 nucleus is 62.91367 amu.

Find the composition of the copper-63 nucleus and determine the combined mass of its components.

Copper has 29 protons and copper-63 also has (63 – 29) 34 neutrons.

The mass of a proton is 1.00728 amu and a neutron is 1.00867 amu.

The combined mass is calculated:

29 protons(1.00728 amu/proton) + 34 neutrons(1.00867 amu/neutron)

or

63.50590 amu

Calculate the mass defect.

Dm = 63.50590 amu – 62.91367 amu = 0.59223 amu

Conversion of Mass Defect into Energy

To convert the mass defect into energy:

Convert the mass defect into kilograms (1 amu = 1.6606 x 10-27 kg)

Convert the mass defect into its energy equivalent using Einstein’s equation.

Example: Determine the binding energy of the copper-63 atom.

Convert the mass defect (calculated in the previous example) into kg.

(0.59223 amu/nucleus)(1.6606 x 10-27 kg/amu) = 9.8346 x 10-28 kg/nucleus

Convert this mass into energy using DE = Dmc2, where c = 2.9979 x 108 m/s.

E = (9.8346 x 10-28 kg/nucleus)(2.9979 x 108 m/s)2 = 8.8387 x 10-11 J/nucleus

Expressing Nuclear Binding Energy as Energy per Mole of Atoms, or as Energy per Nucleon

The energy calculated in the previous example is the nuclear binding energy. However, nuclear binding energy is often expressed as kJ/mol of nuclei or as MeV/nucleon.

To convert the energy to kJ/mol of nuclei we will simply employ the conversion factors for converting joules into kilojoules (1 kJ = 1000 J) and for converting individual particles into moles of particles (Avogadro’s Number).

(8.8387 x 10-11 J/nucleus)(1 kJ/1000 J)(6.022 x 1023 nuclei/mol) = 5.3227 x 1010 kJ/mol of nuclei

To convert the binding energy to MeV (megaelectron volts) per nucleon we will employ the conversion factor for converting joules into MeV (1 MeV = 1.602 x 10-13 J) and the number of nucleons (protons and neutrons) which make up the nucleus.

(8.8387 x 10-11 J/nucleus)[1 MeV/(1.602 x 10-13 J)](1 nucleus/63 nucleons) = 8.758 MeV/nucleon

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How to calculate the binding energy ???

please explain as if you were explaining it to a kid ??