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

Given ` T = 4.5 xx 10^(9) " year 1 year"= 365.25 xx 8.64 xx 10^(4) s `
` i.e, 1 " year" = 3.156 xx 10^(7)_(s)`
Hence ` T = 4.5 xx 10^(9) xx 3.156 xx 10^(7) s `
` T = 14.202 xx 10^(16) s `
238 g of Uranium consists of ` 6.023 xx 10^(23)` atoms
1 g of Uranium consists of ` ( 6.023 xx 10^(23))/238 ` atoms
`i.e, N = 0.0253 xx 10^(23)` atoms
But activity A = ` lamda N " where" lamda = ( 0.693)/ T `
Hence ` A = ( 0.693 xx 0.0253 xx 10^(23))/(14.202 xx 10^(16)) " dis.s"^(-1)`
i.e, ` A = 0.122 xx 10^(5) " dis.s"^(-1)`
In terms of curie ` A = ( 0.122 xx 10^(5))/(3.7 xx 10^(10)) Ci `
i.e, ` A = 0.03297 xx 10^(-5) Ci`
`or A = 3.297 xx 10^(-7) C i`