Question

Consider a pure sample of a radioactive isotope with a mass number of 52. If the sample has mass of 33 micrograms and the isotope has a half-life of 27.5 x10⁶ years, determine the decay rate for the sample. Give your answer in decays/secondand with 3 significant figures.

Answer 1

mass number of the sample, M = 52

mass of the sample, m = 33X10^-6 g = 33X10^-9 kg

Number of moles in the sample, n = ( m / M) = (33X10^-9)/ (52) = 6.3462 X 10^-10

Number of atoms in the sample, N = (6.023 X 10²³) n = (6.023 X 10²³) X ( 6.3462 X 10^-10 ) = 3.8223 X 10¹⁴

radioactive decay constant ,  lambda = (0.693 / half-life) = ( 0.693 / (27.5 X 10⁶ years)) = ( 0.693 / (27.5 X 10⁶ X 365X24 X3600)) /sec = 7.991 X 10^-16 /sec

decay rate of the sample = N X lambda = (6.3462 X 10^-10 X7.991 X 10^-16) decays/sec = 5.07 X 10^-25 decays /sec (ans)