Question

In: Physics

An ancient club is found that contains 190 g of pure carbon and has an activity...

An ancient club is found that contains 190 g of pure carbon and has an activity of 4.5 decays per second. Determine its age assuming that in living trees the ratio of (14C/12C) atoms is about 1.00 × 10-12. Note that the half life of carbon-14 is 5700 years and the Avogadro number is 6.02 × 1023.

Please answer in years please

Solutions

Expert Solution

First, calculate the decay constant for 14C, which has a half-life of 5700 years.
decay constant=In2/ T1/2
=In2/ (5700 years)
=1.2160x10^-4 y^-1

The number of 14C nuclei can be calculated in two steps.
First, the number of 12C nuclei in 190 g of carbon is
N(12C)= (6.02 x 10^23 nuclei/mol) x (190g)/ 12.0 g/mol
=9.5317x10^24 nuclei


Ratio of 14C to 12C is 1.00 x 10^-12

N<original>(14C) = (1.00 x 10^-12) (6.5317x10^24)
= 9.5317x 10^12 nuclei

Therefore, the initial activity of the sample is
R<o>= decay constant x N<o>
=(1.216x10^-4 y^-1)(9.5317x 10^12 nuclei)
= 11.5905x10^8 decays/y

Now calculate the age of the ancient club using Equation R=(R<o>)(e^(-decay constant x time), which relates the activity R at any time t to the initial activity R<o>:
R = R<o>e^(-decay constant x t)
R/ R<o> =e^(-decay constant x t)

Given that R=6(3.1526x10^7) decays/y.
We found that R<o> = 11.5905x10^8 decays/y.
Calculate t by taking the natural logarithm of both sides of the last equation:

ln(R/R<o>)=In e^(-decay constant x t)
-decay constant x t = ln(R/R<o>)
-1.216x10^-4 t= -1.81278
t=14907.762 years

Hope it will help you.

please rate the answer.


Related Solutions

An ancient club is found that contains 100 g of pure carbon and has an activity...
An ancient club is found that contains 100 g of pure carbon and has an activity of 6 decays per second. Determine its age assuming that in living trees the ratio of 14C/12C atoms is about 1.10 × 10-12. Note that the half life of carbon-14 is 5700 years and the Avogadro number is 6.02 × 1023.
An ancient club is found that contains 150 g of pure carbon and has an activity...
An ancient club is found that contains 150 g of pure carbon and has an activity of 5.5 decays per second. Determine its age assuming that in living trees the ratio of 14C/12C atoms is about 1.00 x 10^-12 . Note that the half life of carbon-14 is 5700 years and the Avogadro number is 6.02 x 10^23 .
An ancient wooden club is found that contains 80 g of carbon and has an activity...
An ancient wooden club is found that contains 80 g of carbon and has an activity of 7.5 decays per second. Determine its age assuming that in living trees the ratio of 14C/12C atoms is about 1.3×10−12.
An ancient wooden club is found that contains 68 g of carbon and has an activity...
An ancient wooden club is found that contains 68 g of carbon and has an activity of 8.4 decays per second . Determine its age assuming that in living trees the ratio of 14C/12C atoms is about 1.3×10?12.
An ancient wooden club is found that contains 280g of carbon and has an activity of...
An ancient wooden club is found that contains 280g of carbon and has an activity of 7.3 decays per second. Determine its age assuming that in living trees the ratio of 14C/12C atoms is about 1.3
A pure gas contains 81.71% carbon and 18.29% hydrogen by mass. Its density is 1.97 g/L
A pure gas contains 81.71% carbon and 18.29% hydrogen by mass. Its density is 1.97 g/L
An old piece of wood has a carbon mass of 124 g and an activity of...
An old piece of wood has a carbon mass of 124 g and an activity of 13 Bq. How old is the song? The radioactive isotope of natural carbon has f = 1.3⋅10−12 parts and has a half life of 5730 years. The average for the year is 3.156⋅107 seconds. Please give your answer in years (ie a).
An archeological specimen containing 9.42 g of carbon has an activity of 1.58 Bq. How old...
An archeological specimen containing 9.42 g of carbon has an activity of 1.58 Bq. How old (in years) is the specimen? Do not enter unit.
a 0.580 g sample of a compound containing only carbon and hydrogen contains .480 g of...
a 0.580 g sample of a compound containing only carbon and hydrogen contains .480 g of carbon and .100g of hydrogen. At STP 33.6mL of the gas has a mass of .087g. What is the molecular formula for the compound? The answer should be C4H10. Please explain with steps. Thank you.
An archaeologist finds some ancient jewelry made from bone. The jewelry has a carbon mass of...
An archaeologist finds some ancient jewelry made from bone. The jewelry has a carbon mass of 163 g (HINT: Assume all the carbon is 12C and determine the number of atoms) and careful measurements show that the remaining 14C has a current decay rate of 21 decays/s. Determine the age of the bone (and presumably the jewelry). Remember, the ratio of 14C to 12C when the animal died was 1.3×10-12 & the half-life of 14C is 5730 y. age of...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT