Ch.6 - Electronic Structure of Atoms

Brown - Chemistry: The Central Science 15th Edition

Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook

Brown 15th Edition

Ch.6 - Electronic Structure of Atoms

Problem 26a

Chapter 6, Problem 26a

(a) A green laser pointer emits light with a wavelength of 532 nm. What is the frequency of this light?

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Identify the relationship between wavelength and frequency using the equation: \( c = \lambda \nu \), where \( c \) is the speed of light (approximately \( 3.00 \times 10^8 \) m/s), \( \lambda \) is the wavelength, and \( \nu \) is the frequency.

Convert the given wavelength from nanometers to meters. Since 1 nm = \( 1 \times 10^{-9} \) m, multiply 532 nm by \( 1 \times 10^{-9} \) to convert it to meters.

Rearrange the equation \( c = \lambda \nu \) to solve for frequency \( \nu \): \( \nu = \frac{c}{\lambda} \).

Substitute the values for \( c \) and \( \lambda \) into the equation: \( \nu = \frac{3.00 \times 10^8 \text{ m/s}}{\lambda} \), where \( \lambda \) is the wavelength in meters.

Calculate the frequency \( \nu \) using the substituted values to find the frequency of the green laser light.

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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 these two properties of light.

Units of Measurement

In physics and chemistry, it is essential to use consistent units when performing calculations. Wavelength is often measured in nanometers (nm), where 1 nm = 1 x 10^-9 meters. Frequency is measured in hertz (Hz), which is equivalent to cycles per second. Converting units correctly ensures accurate calculations and results.

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 wavelength of 532 nm falls within the visible spectrum, specifically in the green region. Understanding where a wavelength lies in the spectrum helps in identifying its properties and applications.

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Electromagnetic Spectrum

Related Practice

Textbook Question

(a) Calculate the energy of a photon of electromagnetic radiation whose frequency is 2.94 × 10¹⁴ s^-1.

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Textbook Question

(b) Calculate the energy of a photon of radiation whose wavelength is 413 nm.

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Textbook Question

If human height were quantized in 1-foot increments, what would happen to the height of a child as she grew up?

a. The child’s height would never change.

b. The child’s height would continuously get greater.

c. The child’s height would increase in “jumps” of 1 foot at a time.

d. The child’s height would increase in jumps of 6 inches.

Textbook Question

(c) The laser pointer emits light because electrons in the material are excited (by a battery) from their ground state to an upper excited state. When the electrons return to the ground state, they lose the excess energy in the form of 532-nm photons. What is the energy gap between the ground state and excited state in the laser material?

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Textbook Question

(b) What is the energy of one of these photons?

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