Question

one gram radium with atomic weight 226emits 4(10 to the power of10) particles per second.the half life of radium

Answer 1

given weight of radium = 1 g
molecular weight of radium = 226g/mol
so, number of moles = 1/226
number of atoms = number of moles × 6.023 × 10²³
= 1/226 ×6.023 × 10²³
number of particles emits per second = 4 × 10¹⁰ e.g., decay rate = 4 × 10¹⁰ s⁻¹
Now, use formula
-dN/dt = λN
4 × 10¹⁰ s⁻¹ = λ × 1/226 × 6.023 × 10²³
λ = 4 × 10¹⁰ × 226/6.023 × 10²³
= 904/6.023 × 10⁻¹³

Now, half life = 0.693/λ = 0.693/(904/6.023 × 10⁻¹³)
= 0.693 × 6.023 × 10¹³/904
= 693 × 6.023 × 10¹⁰/904
= 4.61 × 10¹⁰ second