Ch.6 - Electronic Structure of Atoms

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.6 - Electronic Structure of Atoms

Problem 82b

Chapter 6, Problem 82b

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)?

Verified step by step guidance

First, we need to find the wavelength of the light emitted by the calcium atoms. The color orange corresponds to a wavelength of approximately 600 nm in the visible light spectrum.

Next, we convert the wavelength from nanometers to meters by multiplying by 1x10^-9. This is because the speed of light equation and Planck's equation, which we will use in the next steps, require the wavelength to be in meters.

Then, we use the speed of light equation, c = λν, to find the frequency (ν) of the light. Here, c is the speed of light (3.00 x 10^8 m/s), λ is the wavelength we just found, and ν is the frequency. Rearrange the equation to solve for ν: ν = c/λ.

After finding the frequency, we use Planck's equation, E = hν, to find the energy (E) of one photon. Here, h is Planck's constant (6.626 x 10^-34 J*s), and ν is the frequency we just found.

Finally, to find the energy of 1.00 mol of these photons, we multiply the energy of one photon by Avogadro's number (6.022 x 10^23), because there are that many photons in one mole. So, the energy of 1.00 mol of photons = E * Avogadro's number.

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Key Concepts

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

Flame Test

The flame test is a qualitative analysis technique used to identify the presence of certain metal ions based on the color of the flame produced when the sample is heated. Different elements emit characteristic colors when their electrons are excited by heat and then return to their ground state, releasing energy in the form of light. For example, calcium produces an orange flame, which is indicative of its presence.

Photon Energy

Photon energy is the energy carried by a single photon, which can be calculated using the equation E = hν, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), and ν (nu) is the frequency of the light. The energy of photons is directly proportional to their frequency and inversely proportional to their wavelength, meaning higher frequency light (like blue) has more energy than lower frequency light (like red).

Mole and Avogadro's Number

A mole is a unit in chemistry that represents 6.022 x 10^23 entities, known as Avogadro's number. This concept allows chemists to count particles, such as atoms or molecules, in a given sample by relating macroscopic quantities to the number of particles. When calculating the energy of 1.00 mol of photons, one would multiply the energy of a single photon by Avogadro's number to find the total energy for the mole of photons.

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Related Practice

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. (c) Calculate the energy gap between the excited and ground states for the calcium atom.

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.

600

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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

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 (a) Determine which of these emissions occur in the ultraviolet part of the spectrum.

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?

489

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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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