Question

Calculate the mass defect of the boron nucleus 11 5B. The mass of neutral 11 5B is equal to 11.009305 atomic mass units. Express your answer in atomic mass units to four significant figures.

Part B

Calculate the binding energy E of the boron nucleus 11 5B (1eV=1.602×10−19J). Express your answer in millions of electron volts to four significant figures.

Part C

Calculate the binding energy per nucleon of the boron nucleus 11 5B. Express your answer in millions of electron volts to four significant figures.

Part D

Calculate the mass defect of the helium nucleus 32He. The mass of neutral 32He is given by MHe=3.016029amu. Express your answer in atomic mass units to four significant figures.

Part E

Calculate the binding energy E of the helium nucleus 32He (1eV=1.602×10−19J). Express your answer in millions of electron volts to four significant figures.

Part F

Calculate the binding energy per nucleon of the helium nucleus 32He. Express your answer in millions of electron volts to four significant figures

Answer 1

• Part A

  Mass defect ¹¹₅B

  Mass defect =( Combined mass of protons and neutrons in the atom )- (actual mass of the atom)

  No. of protons in ¹¹₅B=5

  Mass of 1 proton = 1.00728 amu

  Mass of protons in¹¹₅B= 5 * 1.00728 amu =5.0364 amu

  No. of neutrons in   ¹¹₅B =6

  Mass of 1 neutron = 1.008665 amu

  Mass of neutrons in   ¹¹₅B = 6 * 1.008665 amu = 6.05199 amu

  Combined mass of protons and neutrons in ¹¹₅B= 5.0364 amu +6.05199 amu

  = 11.08839 amu

  Actual atomic mass of ¹¹₅B=11.009305 amu

  Therefore,

  Mass defect = ( Combined mass of protons and neutrons in the ¹¹₅B )- (actual atomic mass of the ¹¹₅B)

  = 11.08839 amu -11.009305 amu

  = 0.079085 amu

  Part B

  Binding energy per nucleus

  Mass defect per nucleus, m = 0.079085 amu / nucleus = 0.079085 amu *[1.6605387×10⁻²⁷ kg / 1 amu] / nucleus

  =1.31323  *10^-28 kg/ nucleus

  Converting mass to energy using Einsten's equation ,E =mc², where c = 2.998 x 10⁸ m/s

  E =mc²

  =(1.31323  *10^-28 kg/ nucleus)*(2.998 x 10⁸ m / s)²

  = 1.8033*10^-11 J / nucleus

  {1 MeV = 1.602*10^-13 J ; 1J =1 / 1.602*10^-13 MeV ]

  Therefore,

  1.8033*10^-11 J / nucleus = [ 1.8033*10^-11 J * (1 MeV /   1.602*10^-13 J)] / nucleus

  =112.6 MeV/ nucleus

  Part C

  Binding  energy per nucleon of ¹¹₅B

  No. of nucleons in ¹¹₅B= 11

  Binding energy per nucleon 112.6 MeV / 11  nucleons

  = 10.23  MeV/ nucleon

• Part D

  Mass defect ₂³He

  Mass defect =( Combined mass of protons and neutrons in the atom )- (actual mass of the atom)

  No. of protons in  ₂³He=2

  Mass of 1 proton = 1.00728 amu

  Mass of protons in  ₂³He= 2 * 1.00728 amu = 2.01456 amu

  No. of neutrons in   ₂³He =1

  Mass of 1 neutron = 1.008665 amu

  Mass of neutrons in   ₂³He = 1 * 1.008665 amu =1.008665 amu

  Combined mass of protons and neutrons in   ₂³He= 2.01456amu +1.008665

  = 3.023225 amu

  Actual atomic mass of ₂³He=3.016029 amu

  Therefore,

  Mass defect = ( Combined mass of protons and neutrons in the ₂³He- (actual atomic mass of the ₂³He)

  = 3.023225 amu - 3.016029 amu

  = 0.007196 amu

  Part E

  Binding energy per nucleus

  Mass defect per nucleus, m = 0.007196 amu / nucleus = 0.007196 amu *[1.6605387×10⁻²⁷ kg / 1 amu] / nucleus

  =1.194923 *10^-29 kg/ nucleus

  Converting mass to energy using Einsten's equation ,E =mc², where c = 2.998 x 10⁸ m/s

  E =mc²

  =(1.194923 *10^-29 kg/ nucleus)*(2.998 x 10⁸ m / s)²

  = 1.073997*10^-12 J / nucleus

  {1 MeV = 1.602*10^-13 J ; 1J =1 / 1.602*10^-13 MeV ]

  Therefore,

  1.073997*10^-12 J / nucleus = [ 1.073997*10^-12 J * (1 MeV /   1.602*10^-13 J)] / nucleus

  =6.704 MeV/ nucleus

  Part F

  Binding  energy per nucleon of  ₂³He

  No. of nucleons in ₂³He= 3

  Binding energy per nucleon =6.704 MeV/ 3 nucleons

  = 2.235 MeV/ nucleon