Ch.6 - Electronic Structure of Atoms

Brown - Chemistry: The Central Science 15th Edition

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Brown 15th Edition

Ch.6 - Electronic Structure of Atoms

Problem 26c

Chapter 6, Problem 26c

(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?

Verified step by step guidance

Identify the wavelength of the photon emitted, which is given as 532 nm.

Convert the wavelength from nanometers to meters by multiplying by \(10^{-9}\).

Use the equation for the energy of a photon, \(E = \frac{hc}{\lambda}\), where \(h\) is Planck's constant (\(6.626 \times 10^{-34}\) J·s), \(c\) is the speed of light (\(3.00 \times 10^8\) m/s), and \(\lambda\) is the wavelength in meters.

Substitute the values of \(h\), \(c\), and \(\lambda\) into the equation to calculate the energy \(E\) in joules.

The calculated energy represents the energy gap between the ground state and the excited state in the laser material.

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Key Concepts

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

Energy Levels in Atoms

Atoms have quantized energy levels where electrons reside. The ground state is the lowest energy level, while excited states are higher energy levels. When electrons absorb energy, they can transition to these excited states. The difference in energy between these levels determines the energy of the photons emitted when electrons return to the ground state.

Photon Energy and Wavelength

The energy of a photon is inversely related to its wavelength, described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. For the laser pointer emitting 532-nm photons, this relationship allows us to calculate the energy of the emitted photons, which corresponds to the energy gap between the excited and ground states.

Calculating Energy Gaps

To find the energy gap between the ground state and excited state, one can use the energy of the emitted photon. By substituting the wavelength of the emitted light into the photon energy equation, we can determine the energy difference. This calculation is essential for understanding the transitions of electrons in the laser material and the efficiency of the laser process.

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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.

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Textbook Question

An AM radio station broadcasts at 1010 kHz, and its FM partner broadcasts at 98.3 MHz. Calculate and compare the energy of the photons emitted by these two radio stations.

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Textbook Question

One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (c) How many photons are in a 1.00 mJ burst of this radiation?

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