Half life of U-238 undergoing `alpha` decay is `4.5 xx 10^(9)` years. What is the activity of one gram of U-238 sample ?

Explanation

`T_(1//2) = 4.5 xx 10^(9)` years
`T_(1//2) = 4.5 xx 10^(9) xx 365 xx 24 xx 60 xx 60 = 1.42 xx 10^(17)s`
Mass of sample, m = 1g 238 gram contains `6.023 xx 10^(23)` nuclei.
Hence, no of nucleic 1 gram sample, `N = (6.023 xx 10^(23) xx 1)/(238) = 2.53 xx 10^(21)`
`R = lambda N = (0.693)/(T_(1//2)) xx N = (0.693 xx 2.53 xx 10^(21))/(1.42 xx 10^(17))`
`R = 1.23 xx 10^(4) Bq`