Question

In: Chemistry

calculate the mass defect and nuclear binding energy per nucleon (in mev) for c-16, a radioactive...

calculate the mass defect and nuclear binding energy per nucleon (in mev) for c-16, a radioactive isotope of carbon with a mass of 16.014701 amu.

Expert Solution

For ₆C¹⁶

no of protons in ₆C¹⁶ = 6

no. of neutrons = 16- 6 = 10

mass of proton = 1.00728 amu

mass of 6 protons = 6 x 1.00728 = 6.04368 amu

mass of neutron = 1.00867 amu

mass of 10 neutrons = 10 x 1.00867 = 10.0867 amu

total mass of ₆C¹⁶ = 6 protons mass + 10 neutrons mass

= 6.04368 amu + 10.0867 amu

= 16.13038 amu

Actual mass of ₆C¹⁶ = 16.014701 amu.

mass defect = calculated mass - actual mass

= 16.13038 amu - 16.014701 amu.

= 0.115679 amu

1 amu = 931.5 MeV

0.115679 amu = 0.115679 x 931.5 MeV = 107.75 MeV

Mass defect = 0.115679 amu = 107.75 MeV

Binding Energy = mass defect in amu x 931.5 MeV

= 0.115679 amu x 931.5 MeV

= 107.7549 MeV

Nuclear binding energy per nucleon = Binding Energy/ A ( A = mass number = protons + neutrons = 16)

= 107.7549 / 16

= 6.734 MeV

Nuclear binding energy per nucleon = 6.734 MeV

queen_honey_blossom answered 6 months ago

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