Question

Calculate the activity of 30 g of radium-226 in Bq and mCi. ( The half-life of radium-226 is 1600yeras.) Ci ( = 3.7 times10^10Bq)

Answer 1

Atomic mass of radium is 226.

226g of radium contain avogadro number (6.022X10²³  ) of radium atoms.

30g contain (6.022 X 10²³ ​/226) X 30 = 8 X 10²² ​atoms.

Activity is related to half-life as             Activity= 0.693 X N/ T_1/2 Bq

Substituting, Activity = 0.693 X 8 X 10²² ​/ (1600 X 365 X 24 X 60 X 60)

                                 = 1.76 X 10¹⁵ Bq

Now to express in Ci, Activity = 1.76 X 10¹⁵ ​/ 3.7 X 10¹⁰ ​Ci

                                              = 4.756 X 10 ⁴​Ci

                                               = 4.756 X 10⁷ mCi