A cylindrical jar 10 cm in diameter and 15 cm tall is full of old copper pennies. Estimate the

step 1 Hello and welcome to this video solution of numerate Here we are given a cylinder having diamete

A cylindrical jar 10 cm in diameter and 15 cm tall is full...

Key Concepts

Valence Electrons of Copper

Understanding the valence electrons in copper involves knowing its electron configuration. Copper (atomic number 29) typically contributes one electron from its 4s orbital as the valence electron, though in some contexts the d electrons may also play a role. This concept connects atomic structure with macroscopic properties, helping to bridge the gap between a bulk quantity of material and its underlying atomic characteristics.

Packing Efficiency

Packing efficiency refers to how densely objects can be arranged within a given volume. When objects like pennies are randomly packed in a container, they do not fill the entire available volume because of the empty spaces in between. Recognizing and accounting for this efficiency is important for accurately estimating the number of individual items in a container.

Avogadro's Number

Avogadro's number, which is approximately 6.02 × 10^23, is used to convert between the number of moles of a substance and the number of atoms or molecules. In estimation problems like this, after determining the mass of copper present, Avogadro's number allows one to estimate the total number of copper atoms, which is a key step in determining the number of valence electrons.

Cylindrical Volume Calculation

This concept involves determining the volume of a cylinder using its dimensions. The formula ?r²h provides the total space available inside the cylindrical jar, which is fundamental when estimating how many objects—or in this case, pennies—can be accommodated. Understanding this formula is crucial in many geometric and physical estimation problems.

Fermi Estimation

Fermi estimation is a technique used to make rough approximations and order-of-magnitude calculations with limited data. It involves breaking down a complex problem into several easier-to-estimate parts and combining them. In this problem, Fermi estimation is applied to approximate the number of pennies, the copper content within each penny, and ultimately the total number of valence electrons in the jar.

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