Ch. 01 - Introduction, Measurement, Estimating

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 01 - Introduction, Measurement, Estimating

Problem 59

Chapter 1, Problem 59

One mole of atoms consists of 6.02 x 10²³ individual atoms. If a mole of atoms were spread uniformly over the Earth's surface, how many atoms would there be per square meter?

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Determine the total number of atoms in one mole using Avogadro's number, which is $6.02 \times 10^{23}$ atoms.

Find the surface area of the Earth. The formula for the surface area of a sphere is $4 \pi R^2$, where $R$ is the radius of the Earth. Use $R \approx 6.37 \times 10^6$ meters.

Calculate the Earth's surface area by substituting $R$ into the formula $4 \pi R^2$.

Divide the total number of atoms in one mole ($6.02 \times 10^{23}$) by the Earth's surface area (calculated in the previous step) to find the number of atoms per square meter.

Express the result in scientific notation to represent the number of atoms per square meter uniformly distributed over the Earth's surface.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Avogadro's Number

Avogadro's Number, approximately 6.02 x 10²³, is the number of atoms, ions, or molecules in one mole of a substance. This constant is fundamental in chemistry and physics for converting between the macroscopic scale of substances and the microscopic scale of individual particles.

Surface Area of the Earth

The Earth's surface area is approximately 510 million square kilometers, or 5.1 x 10¹⁴ square meters. Understanding the total surface area is crucial for calculating how many atoms would be distributed per square meter when one mole of atoms is spread uniformly across the planet.

Uniform Distribution

Uniform distribution refers to spreading a quantity evenly across a given area. In this context, it means that if one mole of atoms is spread over the Earth's surface, each square meter would receive an equal number of atoms, allowing for straightforward calculations of density per unit area.

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Textbook Question

The speed v of an object is given by the equation v = At³ ― Bt, where t refers to time. What are the SI units for the constants A and B?

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Textbook Question

Many sailboats are docked at a marina 4.4 km away on the opposite side of a lake. You stare at one of the sailboats because, when you are lying flat at the water's edge, you can just see its deck but none of the side of the sailboat. You then go to that sailboat on the other side of the lake and measure that the deck is 1.5 m above the level of the water. Using Fig. 1–14, where h = 1.5 m , estimate the radius R of the Earth.

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Textbook Question

The following formula estimates an average person's lung capacity V (in liters, where 1 L = 10³ cm³): V = 4.1H ― 0.018A ―2.7, where H and A are the person's height (in meters) and age (in years), respectively. In this formula, what are the units of the numbers 4.1, 0.018, and 2.7?

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Textbook Question

Show that the following combination of the three fundamental constants of nature that we used in Example 1–10 (that is G, c, and h) forms a quantity with the dimensions of time: tₚ = $\sqrt{G h}$ /c⁵. This quantity, tₚ, is called the Planck time and is thought to be the earliest time, after the creation of the Universe, at which the currently known laws of physics can be applied.

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