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Chapter 5: Problem 14

What is the approximate size (in \(\mathrm{cm}\) ) of an atom?

Short Answer

Expert verified
The approximate size of an atom is 1 to 2 imes 10^{-8} cm.

Step by step solution

01

Understanding Atomic Dimensions

Atoms are extremely small, often measuring in the range of picometers (pm) to angstroms (脜). Most often, the size of an atom is given as 1 to 2 angstroms, where 1 angstrom is equivalent to approximately 0.1 nanometers (nm) or 1 imes 10^{-10} meters.
02

Conversion of Angstroms to Centimeters

To find the size of an atom in centimeters, we need to convert angstroms to centimeters. Since 1 meter equals 100 centimeters, and 1 angstrom equals 1 imes 10^{-10} meters, we have: 1 脜 = 1 imes 10^{-10} m = 1 imes 10^{-10} imes 100 cm = 1 imes 10^{-8} cm.
03

Estimating the Atom Size in Centimeters

Considering an atom size of about 1 to 2 angstroms, the size in centimeters would be: 1 to 2 脜 = 1 imes 10^{-8} cm to 2 imes 10^{-8} cm.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Angstrom
The angstrom, symbolized as 脜, is a unit of length used for measuring very small distances, especially at the atomic scale. It is named after the Swedish scientist Anders Jonas 脜ngstr枚m, who conducted pioneering work in the field of spectroscopy. The angstrom is often used to express atomic dimensions, such as bond lengths and atomic radii.
To put it into perspective:
  • 1 脜 = 1 脳 10^{-10} meters
  • 1 脜 = 0.1 nanometers
Given its scale, the angstrom is an ideal unit for expressing the size of atoms, which usually measure between 1 to 2 angstroms in diameter. This makes it a practical choice for scientists working to describe atomic structures using a standardized unit that aligns with the dimensions being observed.
Conversion Between Units
Converting units is a crucial skill in science to maintain consistency and accuracy in measurements. When measuring atomic sizes, converting from angstroms to centimeters can be particularly helpful for integrating data with other macroscopic measurements.
To convert angstroms (脜) to centimeters (cm):
  • Start with the conversion factor: 1 脜 = 1 脳 10^{-10} meters (m)
  • Since 1 meter = 100 centimeters, multiply the conversion factor 1 脜 = 1 脳 10^{-10} m by 100 to convert to centimeters.
  • You end up with: 1 脜 = 1 脳 10^{-8} cm
This simple conversion reflects the incredibly small scale of atoms when communicated in more common length units, highlighting the difference in magnitude between atomic dimensions and everyday objects.
Estimating Atomic Size
Estimating the size of an atom involves understanding both its scale and behavior. Atoms, the building blocks of matter, are not solid spheres but rather consist of a nucleus surrounded by an electron cloud. This cloud determines the apparent size of the atom.
Typically:
  • Atoms range from about 1 to 2 angstroms in diameter, depending on the element.
  • Chemical interactions and the atomic number influence these sizes.
Estimating atomic size in centimeters involves using the calculation from the previous conversion process. For example:
  • A typical atom measuring 1 脜 converts to an approximate size of 1 脳 10^{-8} cm.
  • An atom measuring 2 脜 would convert to about 2 脳 10^{-8} cm.
This process helps scientists relate the minuscule dimensions of atoms to measurable quantities in experimental contexts.

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Most popular questions from this chapter

Which orbital in each of the following pairs has the larger size? (a) \(2 s\) or \(3 s\) (b) \(2 p_{x}\) or \(3 p_{x}\) (c) \(2 p_{x}\) or \(2 p_{v}\) (d) \(4 p_{\mathrm{y}}\) or \(4 p_{z}\)

State the maximum number of electrons that can occupy each of the following orbitals: (a) 1s (b) \(2 p\) (c) \(3 d\) (d) \(4 f\)

Calculate the atomic mass for lithium given the following data for its natural isotopes: $$ \begin{array}{rrr} { }^{6} \mathrm{Li} & 6.015 \mathrm{amu} & 7.42 \% \\ { }^{7} \mathrm{Li} & 7.016 \mathrm{amu} & 92.58 \% \end{array} $$

Draw a filling diagram and predict the sublevel that follows \(4 s\) s.

Gallium occurs naturally as \({ }^{69} \mathrm{Ga}\) and \({ }^{71} \mathrm{Ga}\). Given the mass and abundance of gallium- \(69(68.92\) amu and \(60.10 \%)\), what is the isotopic mass of gallium-71?
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