Ch.6 - Electronic Structure of Atoms

Problem 81a1

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?

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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.

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.

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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Identify the specific element that corresponds to each of the following electron configurations and indicate the number of unpaired electrons for each: (d) 3Kr45s24d105p4.

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The following electron configurations represent excited states. Identify the element and write its ground-state condensed electron configuration. (b) 3Ar44s13d104p25p1

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

Textbook Question

If you put 120 volts of electricity through a pickle, the pickle will smoke and start glowing orange-yellow. The light is emitted because sodium ions in the pickle 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.)

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?