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

The binding energy and binding energy per nucleon of iodine-131 can be calculated using the mass defect and the speed of light equation E=mc^2. The mass of iodine-131, the mass of its constituent particles, protons and neutrons, and the speed of light are needed to calculate the binding energy.

Step-by-step explanation:

The binding energy of iodine-131 can be calculated using the mass defect and the speed of light equation: E = mc^2. The binding energy per nucleon can be calculated by dividing the binding energy by the total number of nucleons in the isotope.

The mass defect of iodine-131 can be calculated by subtracting the mass of iodine-131 from the mass of its constituent particles, protons, and neutrons.

The binding energy is then calculated by multiplying the mass defect by the speed of light squared.

The mass of iodine-131 is given as 130.906124 u.

The mass of a proton is approximately 1.00783 u and the mass of a neutron is approximately 1.00867 u.

Using these values, we can calculate the mass of iodine-131 in terms of protons and neutrons.

Iodine-131 has 53 protons and can be rounded to 78 neutrons.

The mass defect is calculated by subtracting the mass of iodine-131 from the combined mass of its protons and neutrons.

The binding energy can then be calculated using the equation E = mc^2, where m is the mass defect and c is the speed of light.

The binding energy per nucleon is calculated by dividing the binding energy by the total number of nucleons in the isotope, which is the sum of protons and neutrons.

Using the calculated values, the binding energy of iodine-131 is approximately 1040.36 MeV and the binding energy per nucleon is approximately 6.92 MeV.