Question

Iodine-131 is a radioactive isotope that is used in the treatment of cancer of the thyroid. The natural tendency of the thyroid to take up iodine creates a pathway for which radiation (β− and γ) that is emitted from this unstable nucleus can be directed onto the cancerous tumor with very little collateral damage to surrounding healthy tissue. Another advantage of the isotope is its relatively short half-life (8 days). Calculate the binding energy of iodine-131 and the binding energy per nucleon. The mass of iodine-131 is 130.906124 u.

Answer 1

Answer:

a) Binding Energy = 1084.266 MeV

b) Binding energy per nucleon = 8.28 MeV

Explanation:

Binding Energy, $BE = \triangle M * 931.5$

Where ΔM = Mass defect of Iodine-131

The mass of iodine-131 = 130.906124 u.

Number of protons in Iodine-131 = 53

Number of neutrons in Iodine-131 = 78

Mass of a proton = 1.007276 u

Mass of neutron = 1.008664 u

Total mass of the 53 protons in Iodine-131 = (53*1.007276)

Total mass of the 53 protons in Iodine-131 =  53.39 u

Total mass of the 78 protons in Iodine-131 = (78*1.008664)

Total mass of the 78 protons in Iodine-131 = 78.68 u

$\triangle M = (53.39 + 78.68) - 130.906124\\\triangle M = 1.164 u$

Binding Energy = 1.164 * 931.5

Binding Energy = 1084.266 MeV

b) Binding Energy per nucleon

The mass of the nucleon of iodine 131 = 130.906124

Binding Energy per nucleon =  1084.266/130.906124

Binding energy per nucleon = 8.28 MeV