Monday, July 2, 2012

What is the half-life (in years) of 44-Ti if a 1.0 ng sample decays initially at a rate of 4.8x 10^3 disintegrations per second?

1 ng = 1*10^-9 g = 4.8*10^3 Bq 
1 g = 4.8*10^12 Bq 

the specific activity of an isotope is found by
A = ln(2)/T1/2 * N/M

with T1/2 = half life in seconds 
N = Avogadro's constant = 6.022*10^23 atoms/mol
M = molecular mass in g = 44

T1/2 = ln(2)*N/(A*M) 

T1/2 = ln(2)*6.022*10^23/(4.8*10^12*44) 
T = 1.976*10^9 s 

T = 1.976*10^9/(365*24*60^2) years 
= 62.65 years
(Wiki says 49 years though) 

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