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 `=1. 41912 xx 10 ^(17) ` seconds
`lamda = ( 0.693)/( T _(1//2)) `
` lamda= ( 0. 693)/( 1. 41912 xx 10 ^(17))`
` lamda = 4.883 xx 10 ^(-18) S ^(-1)`
Number of atoms in 1 gram: `N= ( "Avogadro.s No." xx " mass")/("mass number") = (6.023 xx 10 ^(23) xx 1 )/( 238)`
` N = 2. 5306 xx 10 ^(21)`
Activity: `R = N lamda `
`R = 2. 53 06 xx 10 ^(21) xx 4.883 xx 10 ^(-18)`
`R = 1. 235 xx 10 ^(4) Bq`