The Archaeologist’s Python Challenge

Posted on May 19, 2025 by Administrator Posted in Computer Science, Python - Intermediate, Python Challenges, Solved Challenges

In this challenge, you will write a Python script to help an archaeologist estimate the age of an artefact using Carbon-14 dating. This method is commonly used in archaeology to find out how old organic materials and can be used on objects as old as 60,000 years. By organic materials we mean anything that originate from living organisms including bone, cloth, wood and plant fibers. Carbon-14 dating works by measuring the amount of Carbon-14, a radioactive isotope of carbon, that remains in the object. When an organism dies, it stops taking in new Carbon-14, and the existing Carbon-14 starts to decay at a known rate. By measuring the remaining Carbon-14, scientists can estimate how long ago the organism died.

Python Challenge

Your task is to write a Python script that calculates the age of an artefact based on its remaining Carbon-14 content. The script will include 3 steps:

Step 1: Input

Take as an input from the end user the current ratio of Carbon-14 to Carbon-12 in the artefact. (Note that as Carbon-12 is stable/does not decay over time, the ratio of Carbon-14 to Carbon-12 is pro-rata to the amount of carbon 14 remaining in the organism).

Step 2: Process
Apply the following Carbon-14 dating formula to estimate the age of the artefact.

Assuming the initial Carbon-14 to Carbon-12 ration is 1×10^-12 = 1 ppt (parts per trillion), we can simplify the formula as follows

In the above formula:

The Carbon-14 ratio is expressed on parts per trillion (ppt).
t_1/2 represents the Carbon-14 half-life, in other words the total number of years it takes for half of the radioactive carbon-14 atoms in a sample to decay into nitrogen-14 atoms. The half-life of Carbon-14 is approximately 5,730 years.

Using Python you can calculate a natural logarithm (ln) using math.log() from the math library:

import math
ln2 = math.log(2)
print("ln(2) = " + str(ln2))

Step 3: Output
Output the estimated age (in years) of the artefact.

After implementing your script using the online Python IDE below, you will use your script to estimate the age of the following 2 artefacts:

The Bakhshali manuscript (Carbon-14 Ratio: 0.878 ppt)
Tutankhamun’s tomb (Carbon-14 Ratio: 0.695 ppt)

The Bakhshali manuscript

The Bakhshali manuscript is an ancient Indian mathematical text written on birch bark that was found in 1881 in the village of Bakhshali, Mardan (near Peshawar in present-day Pakistan)

The carbon-14 ratio of the Bakhshali manuscript is 0.878 ppt.

The most recent Carbon dating tests from Oxford University revealed that the Bakshali manuscript dates from 799 – 1102 AD (9th – 11th century).

This means the manuscript would be between approximatively 900 to 1200 years old. Is this what your Python script is estimating?

Tutankhamun’s tomb

Archaeologists have been able to use the Carbon-14 method to estimate the age of a few seeds found in the tomb of the Egyptian Pharaoh Tutankhamun who ruled over Ancient Egypt many thousands of years ago.

The carbon-14 ratio of the seeds: 0.695 ppt

Note that samples from Tutankhamun’s tomb were dated using radiocarbon dating techniques, with some samples dating to around 846 BC and 899 BC. These dates are significantly earlier than the traditionally accepted dates for Tutankhamun’s reign, which is generally placed around 1332–1323 BC.

This would mean that the seeds are approximatively 3,000 years old. Is this what your Python script is estimating?