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 21a

Chapter 6, Problem 21a

A laser pointer used in a lecture hall emits light at 650 nm. What is the frequency of this radiation?

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Identify the given information: the wavelength of the light emitted by the laser pointer is 650 nm.

Convert the wavelength from nanometers to meters for consistency in SI units. Recall that 1 nm = 1 x 10^-9 meters.

Use the speed of light equation: c = λν, where c is the speed of light (approximately 3.00 x 10^8 m/s), λ is the wavelength in meters, and ν is the frequency in Hz.

Rearrange the equation to solve for frequency: ν = c / λ.

Substitute the values for c and λ into the equation to calculate the frequency of the radiation.

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Key Concepts

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

Wavelength and Frequency Relationship

The relationship between wavelength and frequency is described by the equation c = λν, where c is the speed of light (approximately 3.00 x 10^8 m/s), λ is the wavelength in meters, and ν is the frequency in hertz. This equation shows that as the wavelength increases, the frequency decreases, and vice versa. Understanding this relationship is crucial for converting between wavelength and frequency.

Units of Measurement

In this context, wavelength is given in nanometers (nm), which is a common unit for measuring light wavelengths, where 1 nm = 1 x 10^-9 meters. Frequency is measured in hertz (Hz), which represents cycles per second. Converting units correctly is essential for accurate calculations in physics and chemistry.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, including visible light, which ranges from approximately 400 nm (violet) to 700 nm (red). A laser pointer emitting light at 650 nm falls within the visible spectrum, specifically in the red region. Understanding where this wavelength fits in the spectrum helps contextualize its properties and applications.

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Electromagnetic Spectrum

Related Practice

Textbook Question

If human height were quantized in 1-cm increments, what would happen to the height of a child as she grows up: (i) the child's height would never change, (ii) the child's height would continuously increase, (iii) the child's height would increase in jumps of 6 cm, or (iv) the child's height would increase in 'jumps' of 1 cm at a time?

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Textbook Question

(d) What distance does electromagnetic radiation travel in 0.38 ps?

Textbook Question

(b) What is the wavelength of radiation that has a frequency of 5.50 × 10¹⁴ s^-1?

Textbook Question

A laser pointer used in a lecture hall emits light at 650 nm. Using Figure 6.4, predict the color associated with this wavelength.

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Textbook Question

It is possible to convert radiant energy into electrical energy using photovoltaic cells. Assuming equal efficiency of conversion, would infrared or ultraviolet radiation yield more electrical energy on a per-photon basis?

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