(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An antiques dealer has claimed that a tapestry is2000years old having been loomed sometime in the first century BC. In order to determine the veracity of this claim a sample of Carbon-14 has been taken for dating. In a1gsample,190ngof Carbon-14 were present.

The half-life of Carbon-14 is5780 years.

The below graph displays the amount of Carbon-14 present in the environment for the past 2100 years.

Known variables:

Current Carbon-14 present: 190ng

Half life of Carbon-14: 5780 years

Wanted variables:

Age of tapestry (t)

And original amount of Carbon-14 ([itex]N_{0}[/itex])

2. Relevant equations

Taken from Wikipedia.

[itex]\frac{dN}{dt} = -\lambda N[/itex]

"...differential equation, where N is the number of radioactive atoms and λ is a positive number called the decay constant"

[itex]N(t) = N_{0}e^{-\lambda t}[/itex]

"...describes an exponential decay over a timespan t with an initial condition of N0 radioactive atoms at t = 0. Canonically, t is 0 when the decay started. In this case, N0 is the initial number of 14C atoms when the decay started."

3. The attempt at a solution

First I calculated the decay constant of C14.

[itex]0.5 = e^{-\lambda 5780}[/itex]

[itex]\lambda = 1.209681344 x 10^{-4}[/itex]

Since the current amount of C14 is 190ng, the sample cannot be older than ~1550, since there was ~190ng of C14 in the environment at that time.

However, this leaves me with two unknowns, [itex]N_{0}[/itex] and [itex]t[/itex].

If I try to get the original amount of C14:

[itex]N(0) = N_{0}e^{-\lambda 0} = N_{0}e^{0} = N_{0}(1)[/itex]

[itex]N(0) = N_{0}[/itex]???

We've never done Carbon-14 dating before, and everything I've found so far has been from my own research. I feel as though I'm not understanding this correctly, and I'm unsure how to go about solving this.

Any and all guidance would be greatly appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Carbon-14 Dating

**Physics Forums | Science Articles, Homework Help, Discussion**