Solved Numerical Problems of Mass Defect,Binding Energy

binding energy & mass defect

binding energy &mass defect

source : dc.edu.au

Q 1—Atomic mass of ₈O¹⁶ is 16.

Mass of one neutron   =1.00893 amu

Mass of one proton     =1.00757 amu

Mass of one electron   =0.0005486 amu

Calculate its mass defect & binding energy?

₈O¹⁶ have 8p,  8n & 8e

Ans.     Mass of  nucleus         = Mass of 8p +mass of 8n

= 8×1.00757 + 8×1.00893

= 8.06056+8.07144

= 16.1320 a.m.u

Mass of nucleus          = Atomic Mass-Mass of 8e

= 16–8×0.0005486

= 16–0.0043888

= 15.9956112 amu

Mass defect (Δm)        = 16.1320–15.9956

                        (Δm)    = 0.1364 amu Ans.

Binding energy  ( B)         = Δm ×931 MeV

= 0.1364×931

B         = 126.988 MeV

Q 2—Calculate  Δm & B. energy  of ₃₃As⁷⁵. The mass of one proton, one neutron & one electron & atomic mass of ₃₃As⁷⁵ is 1.0073 amu, 1.0087 amu& 0.0055 amu and 74.9216 amu

Ans.     ₃₃As⁷⁵ = 33e, 33p&42n

Mass of nucleus = mass of 33p + mass of 42n

= 33×1.0073+42×1.0087

= 33.2409 +42.3654

= 75.6063 amu

Mass of nucleus = Atomic Mass-Mass of 33e

= 74.9216 –33×0.00055

= 74.9216- 0.01815

= 74.90345 amu

Δm       = 75.6063–74.90345

Δm       = 0.70285 amu

B= Δm×931 MeV

= 0.70285×931

B         = 654.35 MeV Ans

Q 3 —Calculate the Δm & b. energy of ₂He⁴. Its actual atomic mass is 4.0039 amu. The mass of one n& one p together is 2.0165 amu. mass one electron=0.0005486amu

Ans .    ₂He⁴= 2e, 2p&2n

Mass of Nucleus         = at. mass–mass of 2e

= 4.0039–2×0.0005486

= 4.0028 amu

Mass of nucleus          = mass of 2p +mass of 2n

= 2(mass of P+mass of n)

= 2×2.0165

= 4.033 amu

Mass defect (Δm)        = 0.0302 amu  An B       = Δm×931 MeV

= 0.0302×931

= 28.12 MeV.

Q 4—Binding energy per nucleon for an element is 7.14 MeV. If the binding energy of the element is 28.6MeVCalculate the number of nucleons in the nucleus.

Ans.     No. of nucleons =?

B = 28.6MeV

Binding Energy per Nucleon = 7.14MeV

No. of nucleons =  =4 Ans.

Q 5—B. energy of an element is 64 MeV. Binding energy per nucleon is 6.39 MeV. What is the total number of neutrons and protons in the nucleus?

Ans.     No. of nucleons = No. of Protons + No. of Neutrons

B= 64MeV

No. of Nucleons =  =10 Ans

Total no. of neutrons & protons = 10 Ans.

Q 6—B. energy of ₂He⁴ is 28.8 MeV. Calculate Binding energy per nucleon?

Ans.     B = 28.8 MeV

No. of Nucleons in ₂He⁴ =4

Binding energy per nucleon =

=  = 7.2 MeV

Ans =7.2 MeV