Question

Part A How many nuclei of 238 U remain in a rock if the activity registers 650 decays per second? The half-life is 4.468x10 yr. Express your answer using two significant figures. IVO AO . o mi? N nuclei Submit Previous Answers Request Answer

Answer 1

Solution) dN/dt = 650 decays per second

T(1/2) = 4.468×10^(9) yr

N = ?

We have

dN/dt = (Lambda)(N)

Lambda = (ln(2))/(T(1/2))

Converting time in years (yr) to seconds (s)

1 yr = 365 days

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds

T(1/2) = 4.468×10^(9)×365×24×60×60  

T(1/2) = 140902848×10^(9) s

T(1/2) = 1.409×10^(17) s

Lambda = (ln(2))/(T(1/2))

Lambda = (0.693)/(1.409×10^(17))

Lambda = 0.4918×10^(-17)

(dN/dt) = (Lambda)(N)

650 = (0.4918×10^(-17))(N)

N = (650)/(0.4918×10^(-17))

N = 1321.67×10^(17) nuclei