Question

Calculate (in MeV) the total binding energy for 40Ar.

Express your answer using four significant figures.

Calculate (in MeV) the binding energy per nucleon for 40Ar.

Express your answer using three significant figures.

Calculate (in MeV) the total binding energy for 40K.

Express your answer using four significant figures.

Part D

Calculate (in MeV) the binding energy per nucleon for 40K.

Express your answer using three significant figures.

Answer 1

From the periodic table, argon has a proton number 18, so an Ar-40 atom consists of 18 electrons, 18 protons and 40-18=22 neutrons.

You should have been give the masses of electron, proton and neutron - usually in amu (atomic mass units). Using these values:

The mass of 18 electrons = 18 x 0.0005486 amu
The mass of 18 protons = 18 x 1.007277 amu
The mass of 22 neutrons = 22 x 1.008665 amu
The sum of these = 40.3314908 amu

You should have been give the mass of an Ar-40 atom. If not, you have to look it up. From the link it is 39.9623831 amu.

The mass deficit = 40.3314908 - 39.9623831= 0.3691077amu

The binding energy is the mass deficit expressed as an energy (E=mc^2). The quick way to calculate this is to use the standard conversion: 1 amu = 931 MeV.

a) So binding energy = 931 x 0.3691077 = 344MeV

b) Since there are 40 nucleons, binding energy/nucleon = 344/40 = 8.598MeV/nucleon

For 40Ar, the binding energy per nucleaon is 8.60Mev

c) the total binding energy for 40K is 341.5Mev.

d)the total binding energy per nucleon for 40K is 341.5Mev / 40 = 8.5375.