Carbon-14 is radioactive and decays by beta decay with a half-life of 5730 years
ID: 832413 • Letter: C
Question
Carbon-14 is radioactive and decays by beta decay with a half-life of 5730 years. One gram of wood from a tree takes up an initial amount of 1.49 nanograms of carbon-14 at some point in the past (due to photosynthesis using carbon dioxide). This one gram of wood is now measured to have an amount of 0.14 nanograms.
a. Write the nuclear decay reaction for this process.
b. How much time has passed since the carbon-14 was initially taken up?
c. What will the activity level (in counts/sec and also in Curies) of the one gram of wood now?
Explanation / Answer
1)6C14 .........> 7N14 + beta
2)it fallows first order reaction
K1 = 2.303/t log(initial/final)
K1 = 0.693/t1/2
K1 = 0.693/5730
K1 = 1.21*10^-9 year^-1
1.21*10^-9 = 2.303/t log(1.49/0.14)
t = 1954805876.02 years
c)
rate = activity = K[1.49]
Activity = 1.21*10^-9 *1.49
= 1.803*10^-9 counts /year
= 0.05686 counts/sec
3.7*10^10 dps...... 1curie
0.05686 counts/sec............?
= 0.05686 / 3.7*10^10
= 0.015*10^-10 curies