Radiocarbon Dating

2009-12-13 5:38 pm

The practical limit to ages that can be determined by radiocarbon dating is about 4100 yr. in a 41000 yr old sample, what percentage of the original carbon-14 remains?
Please teach me step by step thx!!

更新1:

Btw,if anyone can check my answer for the following question... Sodium-24 emits a gamma raythat has an energy of 0.423 MeV.Assuming that the nucleus is initially at rest,determine the speed with which the nucleus recoils.

更新2:

0.423*10^6eV*1.60*10^-19 =6.768*10^-14 mv=(E/c) (6.768*10^-14)/(398*10-26kg*3.00*10^8m/s) =5.67*10^-3m/s Am i right? Thanks a lot!

更新3:

The mass of the nucleus is 3.98*10^-26kg

更新4:

Sorry, the question should be like this ... not 4100 yrs The practical limit to ages that can be determined by radiocarbon dating is about 41000 yr. in a 41000 yr old sample, what percentage of the original carbon-14 remains?

更新5:

I just asked the teacher. My teacher said i have to find the half-live of carbon-14 to solve it..., But thx for helping me

回答 (1)

六呎將軍

2009-12-13 8:14 pm

✔ 最佳答案

(1) The decay equation:

dN/dt = -kN where k is the decay constant.

Then

dN/N = -kdt

∫dN/N = -∫kdt

ln N = -kt + C where C is a constant

N = N0e-kt where N0 is initial no. of redioactive nucleus

So with e-4100k = 1/2, we have k = (ln 2)/4100

Thus, when t = 41000:

e-41000k = e-10ln 2

= 2-10

which is the fraction of original carbon-14 remains. In percentage, 9.77%

(2) In fact you should use conservation of momentum to solve this question:

Momentum of the gamma ray = E/c

= 0.423 x 106 x 1.6 x 10-19/(3 x 108)

= 2.256 x 10-22 kg m/s

So recoiling speed of nucleus = 2.256 x 10-22/(3.98 x 10-26) = 5568 m/s

2009-12-14 08:58:57 補充：
Anyway, pls. wait and be patient, will ans ASAP.

2009-12-14 14:37:37 補充：
According to the official information, half-life of carbon-14 is 5730 years, so:

With e^(-2730k) = 1/2, we have k = (ln 2)/5730

Thus, when t = 41000:

e^(-41000k) = e^(-7.16ln 2)

= 0.00702

So percentage of original carbon-14 remains is 7.02%

2009-12-15 08:55:45 補充：
Ar, yes, 0.00702 should be 0.702%

參考: Myself

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