Posted by **Leila** on Tuesday, May 7, 2013 at 9:46pm.

An ancient wooden club is found that contains 270g of carbon and has an activity of 8.3 decays per second.

Determine its age assuming that in living trees the ratio of 14C/12C atoms is about 1.3x10^-12?

t= in years

- Physics Need help please -
**Elena**, Wednesday, May 8, 2013 at 8:43am
The decay constant is

λ=ln2/T = 0.693/5730 = 1.209•10⁻⁴ yr⁻¹.

The fraction of ¹⁴C << ¹²C, => we use the atomic weight of ¹²C to find the number of carbon atoms in 270 g:

N= (270/12)•6.022•10²³ =1.35•10²⁵ atoms,

The number of ¹⁴C in the sample of living tree is

N₁₄=1.3•10⁻¹²•1.35•10²⁵ =1.76•10¹³ nuclei.

Decay Law

N=N₀•exp(-λt)

Activity

A= λN,

λN=λN₀•exp(-λt) (1 year= 3.16•10⁷ s),

8.3 = (1.209•10⁻⁴•1.76•10¹³/3.16•10⁷) exp(-1.209•10⁻⁴•t),

exp(-1.209•10⁻⁴•t) =

=8.3•3.16•10⁷/1.209•10⁻⁴•1.76•10¹³)=0.12,

-1.209•10⁻⁴•t = ln0.12 = - 2.095,

t=2.095/1.209•10⁻⁴ = 1.73•10⁴ yr.

## Answer This Question

## Related Questions

- Nuclear physics - 1) An old wooden tool is found to contain only 11.9 percent of...
- Nuclear physics Repost - 1) An old wooden tool is found to contain only 11.9 ...
- Radioactivity - 1) An old wooden tool is found to contain only 11.9 percent of ...
- physicsRadioactivity - A specimen taken from the wrappings of a mummy contains 7...
- Physics Help Please - archaeologist digging at the site of an ancient settlement...
- Physics Help Please! Decay Questions - archaeologist digging at the site of an ...
- physics - A wooden artifact is found in an ancient tomb. Its carbon-14 activity ...
- math - A wooden artifact from an ancient tomb contains 70% of the carbon-14 that...
- MATH 123 - A wooden artifact from an ancient tomb contains 55% of the carbon-14 ...
- Physics - A gram of living plant material with Carbon-14 , decays at a rate of ...

More Related Questions