Final answer:
The stack of pennies equal to Avogadro's number would extend approximately 9.153×10¹⁷ km high. This calculation highlights the enormity of Avogadro's number and the hypothetical stack's height far exceeds even the vast distances within our universe, such as the distance to the Sun and to the nearest star, Proxima Centauri.
Step-by-step explanation:
The student is asking how far a stack of pennies totaling Avogadro's number would reach if placed one atop the other on Earth's surface. To calculate this, we need to know the thickness of one penny and Avogadro's number, which is approximately 6.022×1023. Assuming the thickness of a penny is about 1.52 mm, or 0.00152 meters, we can multiply the thickness by Avogadro's number to find the total length in meters:
L = Thickness of one penny × Avogadro's number
L = 0.00152 m × 6.022×10²³
L = 9.153×10²⁰ m
To convert meters to kilometers, we divide by 1,000:
L = 9.153×10²⁰ m ÷ 1,000 m/km = 9.153×10¹⁷ km
This distance is so vast that it not only surpasses the distance from Earth to the Sun (which is about 150 million km) but also dwarfs the scale when comparing the distances in the universe—such as the distance to Proxima Centauri, our nearest star, which is about 40 trillion km away. The stack of pennies would extend far beyond these cosmic distances, highlighting the vastness of Avogadro's number.