Question

Find the binding energy per nucleon in J and eV for the three following isotopes, given their atomic masses in u:
¹⁹₅B   boron   19.06373 u

a) ______________×10^-12J ____________MeV


³³₁₄Si   silicon   32.97800017 u
b) ______________×10^-12J ____________MeV


²²₆C   carbon   22.0572097 u
c) ______________×10^-12J ____________MeV

^mproton=1.007276466 u
^mneutron=1.008664915 u
u=1.6605×10−27 kg

Answer 1

part a:

number of protons=atomic nuber=5

number of neutrons=atomic mass-atomic number=19-5=14

then total mass=14*mass of neutron+5*mass of proton

=14*1.008664915+5*1.007276466

=19.15769114 u

hence mass difference=theoretical mass-actual mass=19.15769114-19.06373= 0.09396114 u= 0.09396114*1.6605*10^(-27) kg=1.56022473*10^(-28) kg

then binding energy=mass difference*speed of light^2

=1.56022473*10^(-28)*(3*10^8)^2

=1.4042*10^(-11) J

=87.762 MeV

part b:

number of protons=atomic nuber=14

number of neutrons=atomic mass-atomic number=33-14=19

then total mass=19*mass of neutron+14*mass of proton

=19*1.008664915+14*1.007276466

=33.266504 u

hence mass difference=theoretical mass-actual mass=33.266504-32.97800017= 0.28850383 u=4.790606*10^(-28) kg

then binding energy=mass difference*speed of light^2

=4.790606*10^(-28)*(3*10^8)^2=269.47 MeV

part c:

number of protons=atomic nuber=6

number of neutrons=atomic mass-atomic number=22-6=16

then total mass=16*mass of neutron+6*mass of proton

=16*1.008664915+6*1.007276466

=22.1822974 u

hence mass difference=theoretical mass-actual mass=22.1822974 -22.0572097=0.1250877 u=2.077081258*10^(-28) kg

then binding energy=mass difference*speed of light^2

==2.077081258*10^(-28)*(3*10^8)^2
=116.835 MeV