Avogadro's number and Carbon Dating.

LUMS Math Circles, “Avogadro’s number and Carbon Dating” conducted on December 1st, 2023, provided a captivating fusion of Chemistry and Mathematics, skillfully facilitated by Dr. Salman Noshear Arshad of the Chemistry department and Dr. Waqas Ali Azhar from the Mathematics department.

The session commenced with Dr. Salman articulating the fundamental significance of units in our everyday lives, drawing parallels between commonplace metrics such as a 'dozen' of eggs and 'kilograms' of potatoes. Introducing the concept of 'moles' as a unit for quantifying substances, he proceeded to expound upon Avogadro's number, a pivotal aspect in comprehending the quantity of a substance. The distinguished figure Amedeo Avogadro (1776-1856) , a luminary Italian scientist contributed significantly to our understanding of the molecular world, notably through Avogadro's number.

A practical exercise ensued, wherein participants computed the density of various solids, including Iron, Aluminium, and Gold. Dr. Salman substantiated the theoretical discourse by presenting tangible samples of Aluminium and Gold, effectively validating the participants' calculations and highlighting the divergent densities of the two metals.

The nexus between Chemistry and Mathematics was further elucidated by Dr. Waqas, who introduced the concept of pH and underscored its minimal numerical representation. Demonstrating how logarithms facilitate the rational representation of both minute and substantial numerical values, he demystified the pH scale as -log[H], where H signifies the number of hydrogen atoms. Contextualizing the discussion, Dr. Waqas provided insight into the contributions of John Napier (1550-1617), renowned for his revolutionary mechanical calculator, "Napier Bones." The live demonstration of this innovative device captivated the audience, particularly the younger participants.

The zenith of the session unfolded with an exploration of Carbon dating, wherein Dr. Salman expounded upon the principles behind this methodology. Participants were provided with pieces of aged wood and challenged to ascertain their respective ages. The ensuing problem-solving exercises were met with enthusiasm, as participants discovered that some wooden artifacts were a century older than initially presumed.

The event concluded with a formal ceremony, during which certificates were distributed to the participants by distinguished visiting foreign faculty, Dr. Peter Stevenhagen and Dr. Salman Noshear. Armed with certificates and enriched by the day's discoveries, the participants departed from LUMS Math Circles, their curiosity piqued, and their appreciation for the interconnected worlds of Mathematics and Chemistry duly heightened.