Question

(a)

Calculate BE/A (in MeV) for ¹²C. Stable and relatively tightly bound, this nuclide is most of natural carbon. (Assume 1 u = 931.5 MeV/c². Give your answer to at least 2 decimal places.)

answer in MeV

(b)

Calculate BE/A (in MeV) for ¹¹C.

answer in MeV

Is the difference in BE/A between ¹²C and ¹¹C significant? One is stable and common, and the other is unstable and rare. (Assume the difference to be significant if the percent difference between the two values is greater than 5%.)

Yes or No    

Answer 1

a.)

Mass defect is given by:

dm = Mass of Protons in 12C + mass of neutrons in 12C + Mass of electrons in 12C - atomic Mass of 12C

Given that

Atomic mass of 12C = 12 u

Mass of 1 proton = 1.007276467 u

Mass of 1 electron = 9.11*10^-31 kg = 0.000549 amu

Mass of 1 neutron = 1.008664916 u

Number of protons in 12C = 6

Number of neutrons in 12C = 6

Number of electrons in 12C = 6

So,

dm = 6*mp + 6*mn + 6*me - M_12C

dm = 6*1.007276467 + 6*1.008664916 + 6*0.000549 - 12

dm = mass defect = 0.098942298 amu

Binding energy is given by:

E = dm*c^2

c^2 = 931.5 Mev/u

So,

E = (0.098942298u)*(931.5 MeV/u) = 0.098942298*931.5

E = Binding energy = 92.164750587 MeV

Binding energy per nucleon will be:

BE per nucleon = BE/total number of nucleons

Total number of nucleons = 12

BE per nucleon = BE/total number of nucleons = 92.164750587/12

Binding energy per nucleon = 7.68 MeV/nucleon

b.)

Mass defect is given by:

dm = Mass of Protons in 11C + mass of neutrons in 11C + Mass of electrons in 11C - atomic Mass of 11C

here,

Atomic mass of 11C = 11.011433613 u

Number of protons in 11C = 6

Number of neutrons in 11C = 5

Number of electrons in 11C = 6

So,

dm = 6*mp + 5*mn + 6*me - M_11C

dm = 6*1.007276467 + 6*1.008664916 + 6*0.000549 - 11.011433613

dm = mass defect = 0.078843769 amu

now,

E = (0.078843769u)*(931.5 MeV/u) = 0.078843769*931.5

E = Binding energy = 73.4429708235 MeV

Binding energy per nucleon will be:

Total number of nucleons = 11

BE per nucleon = BE/total number of nucleons = 73.4429708235/11 = 6.6766

Binding energy per nucleon = 6.68 MeV/nucleon

c.)

difference in BE/A between 12C and 11C = 7.68 - 6.78 = 1 Mev/nucleon

Since, the percent difference between the two values is greater than 5%.

So, Yes,  difference in BE/A between 12C and 11C significant.

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