Question

The half life of \[\ce{^238_92U}\] undergoing α decay is 4.5 × 10⁹ years. Calculate the activity of 10 g sample of \[\ce{^238_92U}\].

Answer 1

Half-life = 4.5 × 10⁹ years

Mass number = 238

λ = `0.693/T`

= `0.693/(4.5 xx 10^9)` per year

N = `(10 xx 6.02 xx 10^23)/238`

Hence, the activity, A = λN

Or, 

A = `0.693/(4.5 xx 10^9) xx (10 xx 6.02 xx 10^23)/238`

∴ A = 0.0039 × 10¹⁵

= 3.9 × 10¹² per year