The decay constant of ``^238U`is `4.9xx10^-18 s^-1.`(a) What is the avarage-life of``^238U`?(b)What is the half-life of ``^238U`?(c) By what factor does the activity of s ``^238U` sample decreases in `9xx19^9` years?

Answer

A, B, C, D

Explanation

` lambda = 4.9 xx 10^(-18) s^(-1) `
(a ) Average life of
` ^(228) U = (1)/(lambda) = (1)/(49 xx 10^(-18)) `
` = 1/4.9 xx 10^(-16) sec`
`10^(18) /(4.9 xx 365 xx 24 xx 3600) years `
` = (10^(16) /(4.9 xx 365 xx 24 xx 36 ) year
` = 6.47 xx 10^(-7) xx 10^(16)` years
`=6.47 xx 10^7` years
(b) Half of Uranium
`= 0.693/lambda = 0.693/(4.9 xx 10^(-18))`
` = (0.693/ 4.9) xx 10^(18) sec`
`=(0.1414 xx 10^(18))/(365 xx 24 xx 3600)`
`=(1414 xx 10^(12))/(365 xx 24 xx 36)`
`= 4.48 xx 10^(-3) xx 10^(12)`
`= 4.5 xx 10^(9)` years
(c) Since `A = A_0/2^(t/t_(1/2))`
`rArr A_0/A = 2^(9xx10^(9))/(4.5 xx 10^(9)) = 2^2 = 4`