The half-life of ²²⁶ Ra is 1602 y . Determine the activity of 0.1 g of RaCl ₂ , assuming all the radium present is in the form of ²²⁶ Ra . Consider the atomic weight of Ra to be 226 g mol ⁻¹ and that of Cl to be 35.5 g mol ⁻¹ .

Step-by-step solution

Molar mass of RaCl ₂ = 226 + 2 35.5 = 297 g mol ⁻¹ Number of moles of RaCl ₂ = 0.1 297 mol Since each molecule of RaCl ₂ contains one atom of Ra , the number of Ra atoms is: N = 0.1 297 6.022 10²³ 2.028 10²⁰ The half-life of ²²⁶ Ra in seconds is: T_ 1/2 = 1602 365 24 3600 s 5.05 10¹⁰ s The decay constant is given by: = 0.693 T_ 1/2 = 0.693 5.05 10¹⁰ 1.37 10⁻¹¹ s ⁻¹ The activity A of the sample is: A = N = 1.37 10⁻¹¹ 2.028 10²⁰ 2.78 10^9 disintegrations s ⁻¹ Rounding to the nearest given option, the activity is 2.8