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Ch.6 - Electronic Structure of Atoms
Chapter 6, Problem 81a1

Consider the two waves shown here, which we will consider to represent two electromagnetic radiations: (a) What is the wavelength of wave A?
Two electromagnetic wave graphs illustrating wavelength; wave A's wavelength is 2.56 x 10^-6 m.

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1
Identify the wave labeled as 'A' in the image. In this case, it is the wave labeled as (i).
Understand that the wavelength (\
\lambda\
\) is the distance between two consecutive peaks or troughs of the wave.
Observe the given scale in the image, which shows that the distance for wave (ii) is 2.56 x 10^-6 meters.
Count the number of wavelengths for wave (ii) within the given distance. In this case, there are two complete wavelengths for wave (ii).
Since wave (i) has twice the number of wavelengths as wave (ii) within the same distance, the wavelength of wave (i) is half of 2.56 x 10^-6 meters.

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Key Concepts

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

Wavelength

Wavelength is the distance between successive crests (or troughs) of a wave, typically measured in meters. It is a fundamental property of waves, including electromagnetic radiation, and is inversely related to frequency. The longer the wavelength, the lower the frequency, and vice versa. In the context of electromagnetic waves, wavelength determines the type of radiation, such as radio waves, visible light, or gamma rays.
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Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, arranged by wavelength or frequency. It includes a range of waves from radio waves with long wavelengths to gamma rays with very short wavelengths. Understanding where a specific wavelength falls within this spectrum helps in identifying its properties and applications, such as communication, medical imaging, or heating.
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Wave Properties

Waves exhibit several key properties, including amplitude, frequency, and wavelength. Amplitude refers to the height of the wave, indicating its energy, while frequency is the number of cycles that pass a point per second. These properties are interrelated; for instance, a wave's speed is the product of its frequency and wavelength. Understanding these properties is essential for analyzing wave behavior and interactions.
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Related Practice
Textbook Question

(a) What does the term paramagnetism mean? (b) How can one determine experimentally whether a substance is paramagnetic? (c) Which of the following ions would you expect to be paramagnetic: O2+ , N22 -, Li2+ , O22 - ? For those ions that are paramagnetic, determine the number of unpaired electrons.

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Textbook Question

The following do not represent valid ground-state electron configurations for an atom either because they violate the Pauli exclusion principle or because orbitals are not filled in order of increasing energy. Indicate which of these two principles is violated in each example. (b) 3Xe46s3

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Textbook Question

The following electron configurations represent excited states. Identify the element and write its ground-state condensed electron configuration. (b) 3Ne43s13p44p1.

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Textbook Question

Consider the two waves shown here, which we will consider to represent two electromagnetic radiations: (b) What is the frequency of wave A?

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Textbook Question

If a sample of calcium chloride is introduced into a nonluminous flame, the color of the flame turns to orange ('flame test'). The light is emitted because calcium atoms become excited; their return to the ground state results in light emission. (b) What is the energy of 1.00 mol of these photons (a mole of photons is called an Einstein)?

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Textbook Question

Certain elements emit light of a specific wavelength when they are burned or heated in a non-luminous flame. Historically, chemists used such emission wavelengths to determine whether specific elements were present in a sample. Some characteristic wavelengths for a few of the elements are given in the following table: Ag 328.1 nm Fe 372.0 nm Au 267.6 nm K 404.7 nm Ba 455.4 nm Mg 285.2 nm Ca 422.7 nm Na 589.6 nm Cu 324.8 nm Ni 341.5 nm (c) When burned, a sample of an unknown substance is found to emit light of frequency 6.58 * 1014 s-1. Which of these elements is probably in the sample?

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