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E=mc2 - mass energy conversion

Q1.

(a) State what is meant by the binding energy of a nucleus.

The binding energy of a nucleus is the energy needed to separate the nucleus into its constituent nucleons.

(OR the energy released when the nucleus is formed from individual nucleons)

(2 marks)

(b)

(i) The iron isotope

(atomic mass: 55.93493) has a very high binding energy per nucleon.

Calculate its value in MeV.

Use the following data:

mass of proton = 1.00728 u

mass of neutron = 1.00867 u

mass of electron = 0.00055 u

mass defect = mass of nucleus (which equals mass of atom - mass of electrons ) - mass of individual nucleons

Δm = (mass of iron atom - its electrons) - (mass of 26 individual protons + mass of 30 individual neutrons)

Δm = (55.93493 - 26 x 0.00055) u - (26 x 1.00728 + 30 x 1.00867) u

Δm = 55.92063u - (26.18928 + 30.2601)u

Δm = - 0.52875u

This is the mass that is changed becomes the 'binding energy'.

That is the energy that would have to be put into the iron nucleus to pull it into its constituent nucleons.

We use the conversion factor (see bottom row) to change it into MeV equivalent.

EB = 0.52875 x 931.5 = 492.5 MeV

There are 56 nucleons so:

EB /nucleon = 492.5/56 = 8.795 MeV

 

(ii) If the isotope were assembled from its constituent particles, what would be the mass change, in kg, during its formation?

Here we need to convert the mass difference in u into kg - using the conversion factor on the data sheet - that bottom line again!.

0.52875u = 0.52875u x 1.661 x 10-27 kg

mass change = 8.783 x 10-28 kg

(6 marks)

(Total 8 marks)