Question

Medical 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 (ββ- and γγ) 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). The mass of iodine-131 is 130.906124 u,1 u = 931.494 MeV/c22. For the mass of a hydrogen atom, use 1.007825 u. For the mass of a neutron, use 1.008665 u. To convert between amu and MeV, take the rest energy of 1 u to be 931.494 MeV.

1)Calculate the total binding energy of iodine-131

2)Calculate the binding energy per nucleon. (Express your answer to six significant figures.)

Answer 1

Answer:

I. Total nuclear binding energy = 1,103.33MeV.

II. Nuclear binding energy per nucleon = 8.42235MeV

Explanation:

Actual mass of 13153I = 130.906124u

Number of hydrogen atoms (protons) = 53

Number of neutrons = 131-53 = 78

Mass of 53 protons = 53 x 1.007825u = 53.414725u

Mass of 78 neutrons = 78 x 1.008665u = 78.67587u

Theoretical ( calculated) mass of 13153I = 53.414725 + 78.67587 = 132.090595u

Mass defect, ∆m, of 13153I = Theoretical mass – Actual mass = 132.090595 – 130.906124 = 1.184471u

I. Total nuclear binding energy of 13153I = ∆m x 931.494 =1.184471u x 931.494MeV/u = 1,103.33MeV.

II. Nuclear binding energy per nucleon = Total nuclear binding energy/number of nucleons = 1,103.33/53 = 8.42235MeV.

You can convert MeV to Joules using the conversion factor:

1MeV = 1.60218 X 10-13 Joules.