Question

find the radius of each stable isotope

lead- 204

lead-206

lead-207

lead-208

using the nuclear theory the average radius of a nucleus is given by

R=1.2x10^-13 A^1/3 cm

B) what is the natural % abundance for each isotope above

C) what are the weighted R(cm)

D) what is the total weighted R(cm)

E) what is the weightes average R(cm)

F) relative comparison ration =

Answer 1

B) natural % abundance of each isotopes

lead-204 = 1.4% [relative % abundance = 2.7%]

lead-206 = 24.1% [relative % abundance = 46%]

lead-207 = 22.1% [relative % abundance = 42.2%]

lead-208 = 52.4% [relative % abundance = 100%]

C) weighted R(cm)

lead-204 = 1.2 x 10^-13(204)^0.333

               = 7.06 x 10^-13 cm

lead-206 = 1.2 x 10^-13(206)^0.333

               = 7.09 x 10^-13 cm

lead-207 = 1.2 x 10^-13(207)^0.333

               = 7.10 x 10^-13 cm

lead-208 = 1.2 x 10^-13(208)^0.333

               = 7.11 x 10^-13 cm

D) total weighted R(cm) = 2.836 x 10^-12 cm

E) The weightes average = 7.09 x 10^-13 cm

F) relative comparison ratio = Pb-204 : Pb-206 : Pb-207 : Pb-208 = 24.90 : 25.0 : 25.0 : 25.07