Carbon 14, radioactive decay of ocean waters

[cgarr017]

The youngest bottom waters in the North Atlantic had a [delta 14 C] value of approx -70o/oo (o/oo being parts per thousand). Bottom waters in the South Pacific have a [delta 14 C] value of -170o/oo, while bottom waters in the North Pacific had a [delta 14 C] value of -230o/oo.
a)In the [delta 14 C] notation, the specific sample activity is approximately given by 1+([delta 14 C]/1000). Using this fromula, convert these [delta 14 C] values to specific carbon 14 activities. For this i got north atlantic-> 1+ (-70/1000)=0.93, south pacific->0.83, north pacific->0.77.
b)Now, assume that a water mass sinks out of the north atlantic at t=0 with the specific activity based on a [delta 14 C] value of -70o/oo. Using the Radioactive Decay equation N=N0e^-(0.693t/(T1/2)), calculate the "age" of the waters in the south pacific and north pacific. recall that T1/2 is half-life and the half-life of carbon is 5,730 years.
c)The average replacement or residence time for the entire ocean is ~500-1000 years. Please discuss the ages you calculated for north pacific and south pacific waters in the context of this average replacement time.

Now, I'm stuck on part B I'm not sure whether to put the specific activity values in for N or N0. If i put it in for N and then put 0 for N0 as the initial value it doesn't work obviously. i don't know any guidance or assistance would be much appreciated. thanks

 

[nate808]

Hello,

For part B, you would use the specific activity values for N0, as these represent the initial amount of carbon-14 in the water mass. You would then use the specific activity values for N at the different locations (North Pacific and South Pacific) to calculate the age.

For example, for the North Pacific waters, you would use the specific activity value of 0.77 for N0 and the specific activity value of 0.93 for N. This would give you an age of approximately 1,000 years (since the half-life of carbon-14 is 5,730 years).

For the South Pacific waters, you would use the specific activity value of 0.83 for N0 and the specific activity value of 0.93 for N. This would give you an age of approximately 500 years.

In the context of the average replacement time of 500-1000 years, the ages calculated for the North Pacific and South Pacific waters suggest that they are relatively young water masses that have recently sunk from the surface. This is consistent with the [delta 14 C] values, as they are both less negative than the North Atlantic waters, indicating a higher proportion of recently produced carbon-14.

I hope this helps clarify things for you. Let me know if you have any further questions.

 

[Blueshift5]

a) Your calculations for the specific carbon 14 activities are correct.

b) In this case, N0 would represent the initial amount of carbon 14 present in the water mass when it sinks out of the North Atlantic. We can use the specific activity value of 0.93 for this water mass. So, N0 = 0.93.

For the south pacific waters, we can use the specific activity value of 0.83. So, N = 0.83.

For the north pacific waters, we can use the specific activity value of 0.77. So, N = 0.77.

Using the given formula, we can calculate the "age" of these water masses as follows:

For south pacific waters:
N0 = 0.93
N = 0.83
T1/2 = 5,730 years
t = (T1/2/0.693) * ln(N0/N)
= (5,730/0.693) * ln(0.93/0.83)
= 1,000 years

For north pacific waters:
N0 = 0.93
N = 0.77
T1/2 = 5,730 years
t = (T1/2/0.693) * ln(N0/N)
= (5,730/0.693) * ln(0.93/0.77)
= 1,500 years

c) The ages calculated for the north pacific and south pacific waters are significantly longer than the average replacement time of 500-1000 years. This suggests that these water masses have been isolated from the rest of the ocean for a longer period of time, possibly due to deep ocean currents and circulation patterns. This information can be useful in understanding the movement and mixing of ocean waters and their influence on global climate patterns.