Answer to Question #260254 in Inorganic Chemistry for shamsa

Question

3. Nuclear chemistry

1. Calculate the binding energy per nucleon in MeV for the iron isotope with an atomic number of 26 and a mass number of 56, 56Fe26 which has an atomic mass of 55.9349 amu.

2. Calculate:

a. The rate constant for the radioactive disintegration of cobalt-60, an isotope used in cancer therapy. 60Co27 decays with a half-life of 5.2 years to produce 60Ni28.

b. The fraction and the percentage of a sample of the 60Co27 isotope that will remain

after 15 years.

c. How long it takes for a sample of 60Co27 to disintegrate to the extent that only 2 % of the original amount remains?

d. The half-life of 216Po84 is 0.16 s. How long does it take to reduce a sample of it to the negligible amount of 0.000010 % of the original amount (1.0 x 10-7 times the original amount)?

Answer 1

Binding Energy: The amount of energy released when a nucleus is formed from its components.• Mass defect ΔM = Z×M_p + N×M_n-M_AZ= Atomic no., N= No. of neutrons M_p = Mass of proton, M_n = Mass of neutron,M_A= Atomic Mass

Binding Energy = ΔMc² = ΔM × 931.5 MeV

Binding Energy Per Nucleon = ΔMc² = (ΔM ×931.5 MeV)/ (no. of protons + no. of neutrons)

Here ΔM can be calculated from above equation as:

Z=26, N=30, M_p=1.0078 u, M_N= 1.0086 u.

ΔM = 26(1.0078) +30(1.0086)-55.9349ΔM = 0.5259 u

Binding Energy= ΔMc² = 0.5259 × 931.5 MeV = 489.87 MeV

Binding Energy Per Nucleon = (489.87)/56 = 8.74 MeV