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Ch.6 - Electronic Structure of Atoms
Chapter 6, Problem 81b1

Consider the two waves shown here, which we will consider to represent two electromagnetic radiations: (b) What is the frequency of wave A?
Graph showing a wave representing electromagnetic radiation with a wavelength of 3.6 x 10^-9 m.

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1
Identify the given wavelength (λ) of wave A from the image, which is 3.6 x 10^-9 meters.
Recall the speed of light (c) in a vacuum, which is approximately 3.00 x 10^8 meters per second.
Use the relationship between the speed of light, wavelength, and frequency: c = λν, where ν is the frequency.
Rearrange the formula to solve for frequency (ν): ν = c / λ.
Substitute the given values into the equation: ν = (3.00 x 10^8 m/s) / (3.6 x 10^-9 m).

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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. In this case, the wavelength of wave A is given as 3.6 x 10^-9 m, which places it in the electromagnetic spectrum, specifically in the ultraviolet or X-ray region. Understanding wavelength is crucial for calculating other wave properties, such as frequency.
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Frequency

Frequency is the number of cycles of a wave that pass a given point per unit time, usually expressed in hertz (Hz). It is inversely related to wavelength; as wavelength increases, frequency decreases, and vice versa. The relationship between frequency (f) and wavelength (λ) is given by the equation f = c/λ, where c is the speed of light in a vacuum (approximately 3.00 x 10^8 m/s).
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Speed of Light

The speed of light in a vacuum is a fundamental constant of nature, approximately 3.00 x 10^8 m/s. This speed is crucial in electromagnetic wave calculations, as it relates wavelength and frequency. The equation c = fλ shows that the speed of light is equal to the product of frequency and wavelength, allowing for the determination of one property if the others are known.
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Related Practice
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: (a) What is the wavelength 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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Textbook Question

In January 2006, the New Horizons space probe was launched from Earth with the mission to perform a flyby study of Pluto. The arrival at the dwarf planet was estimated to happen after nine years, in 2015. The distance between Earth and Pluto varies depending on the location of the planets in their orbits, but at their closest, the distance is 4.2 billion kilometers (2.6 billion miles). Calculate the minimum amount of time it takes for a transmitted signal from Pluto to reach the Earth.

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