Question

Half-life question with extension?

a museum acquires a rare piece of clothing thought to be from ancient greece. It was discovered in 2010 AD. Testing shows that the percentage of carbon-14 is 72% of what is expected. If the half-life of C-14 is 5730 years. Can the museum substantiate the authenticity of this clothing?

There should be a sort of timeline depicting this transition

Answer 1

Yes! The radio-carbon age of this piece puts it at circa 705 BC.

Explanation:

Rutherford-Soddy Law of Radiodecay:
`N(t) = N_0\exp(-\lambdat);\qquad \lambda = \ln(2)/t_{1/2}`
`t = [\ln(N_0/(N(t))) / ln(2)] t_{1/2}`
Given:
`t_{1/2} = 5730` `Yrs; \qquad N_0/(N(t)) = 1/0.72`

`t = 0.4739t_{1/2} = 2716` Years ago (which is circa 705 BC)

Time period of Ancient Greece, as given in wikipedia, is from circa 1200 BC to circa 600 AD. So circa 705 BC, places this piece of clothing close in history to the Lelantine War (c 710 BC - c 650 BC) of the Archaic Period of Ancient Greece.