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 23

Chapter 6, Problem 23

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.

Verified step by step guidance

Understand the concept of quantization: In physics and chemistry, quantization refers to the idea that certain properties can only take on discrete values rather than a continuous range.

Apply the concept to the problem: If height were quantized in 1-foot increments, it means that height can only increase in whole foot units, not in fractions of a foot.

Consider the implications for growth: As the child grows, her height would not increase smoothly but would instead 'jump' from one quantized level to the next.

Identify the correct option: Since the height increases in discrete 1-foot increments, the correct answer would be the option that describes this behavior.

Conclude with the correct choice: The child's height would increase in 'jumps' of 1 foot at a time, which corresponds to option c.

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Key Concepts

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

Quantization

Quantization refers to the concept that certain properties, such as energy or height in this scenario, can only take on discrete values rather than a continuous range. In the context of human height being quantized in 1-foot increments, it implies that height can only change in specific steps, rather than smoothly or continuously.

Discrete vs. Continuous Changes

Discrete changes occur in distinct steps or increments, while continuous changes happen gradually without interruption. In this question, the quantization of height means that as the child grows, her height would not change smoothly but would instead increase in defined jumps, specifically in 1-foot increments.

Growth Patterns

Growth patterns in children typically involve gradual increases in height, influenced by genetics and nutrition. However, if height were quantized, the growth would be limited to specific increments, leading to a scenario where the child's height would only change at certain points, reflecting a more abrupt growth pattern rather than a smooth transition.

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

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

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

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

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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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(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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