the thallium nucleus is radioactive, with a half-life of approximately 3.0 min. at a given instant, the activity of a certain sample of thallium is 2400 bq. using the concept of half-life, what is the approximate activity of the sample 9 minutes later?

                   7.52E21    (or)   7.52 × 10²¹ C atoms

Data Given:

                 Mass of Diamond  =  0.2 × 0.75  =  0.15 g

                 M.Mass of Diamond  =  12.01 g.mol⁻¹ (as it is purely Carbon)

Step 1: Calculate Moles of Diamond as,

                 Moles  =  Mass ÷ M.Mass

Putting values,

                 Moles  =  0.15 g ÷ 12.01 g.mol⁻¹

                 Moles  =  0.0125 mol

Step 2: Calculate number of Carbon atoms,

As 1 mole of any substance contains 6.022 × 10²³ particles (Avogadro's Number) then the relation for Moles and Number of Carbon atoms can be written as,

                 Moles  =  Number of C Atoms ÷ 6.022 × 10²³ Atoms.mol⁻¹

Solving for Number of C atoms,

                 Number of C atoms  =  Moles × 6.022 × 10²³ Atoms.mol⁻¹

Putting value of moles,

                 Number of C atoms  =  0.0125 mol × 6.022 × 10²³ Atoms.mol⁻¹

                 Number of C atoms  =  7.52 × 10²¹ C atoms