Question

What is the mass of a 1.90-?Ci 146C source? The half-life of 146C is 5730 yr. ?

Express your answer to three significant figures and include the appropriate units.

Answer 1

Given that activity of 14C is

1 Ci = 3.7*10^10 decay/sec

R = 1.90 uCi = 1.90*10^-6 Ci = 1.90*10^-6 Ci*[(3.7*10^10 decay/sec)/1 Ci]

R = 7.03*10^4 decay/sec

Now decay constant is given by:

Thalf = 5730 yr = 1.81*10^11 sec

lambda = 0.693/Thalf = 0.693/(1.81*10^11 sec)

lambda = 3.83*10^-12 sec^-1

Now we know that

R = lambda*N

N = R/lambda = 7.01*10^4/(3.83*10^-12)

N = 1.83*10^16 molecules

mass of N molecules will be

m = N*Mw/Na

Mw = molecular weight of 14C = 14.003 gm

Na = 6.023*10^23

m = 1.83*10^16*14.003/(6.023*10^23)

m = 4.25*10^-7 gm = 4.25*10^-10 kg

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