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E = mc2 - mass energy conversion

Q2.

(a) In the context of an atomic nucleus,

(i) state what is meant by binding energy, and explain how it arises,

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)

The potential energy of the nucleons decreases when they come together under the strong force.(max 2)

(ii) state what is meant by mass difference,

The mass of a nucleus is less that the total mass of its constituent nucleons

Δm - the mass difference is difference between the mass of nucleus and the total mass of the individula nucleons that make it up.

Δm = Z mp + (A – Z) mn – mnucleus (max 2)

(iii) state the relationship between binding energy and mass difference.

Eb = (Δm)c2

OR

Eb is energy equivalent of mass defect using E = mc2

(4 marks MAX)

(b) Calculate the average binding energy per nucleon, in MeV nucleon–1, of the nucleus.

mass of atom = 63.92915 u

mass of proton = 1.00728 u

mass of neutron = 1.00867 u

mass defect = mass of nucleus - mass of individual nucleons

Δm = (63.92915 - 30 x 0.00055) u x - (30 x 1.00728 + 34 x 1.00867) u

Δm = - 0.60053 u

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

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

We use the conversion factor to change it into MeV equivalent. This is on the bottom row of the Data Section for Fundamental Constants and Values.

EB = 0.60053 x 931.5 = 559.4 MeV

There are 64 nucleons so:

EB /nucleon = 559.3/64 = 8.740 MeV

(5 marks)

(c) Why would you expect the zinc nucleus to be very stable?

The zinc nucleus has high value of Eb/nucleon [or it is near maximum of the Eb/nucleon vs A curve]

(1 marks)

(Total 10 marks)