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Ch.6 - Electronic Structure of Atoms
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
All textbooksBrown 14th EditionCh.6 - Electronic Structure of AtomsProblem 25c
Chapter 6, Problem 25c

(c) What wavelength of radiation has photons of energy 6.06 × 10-19 J?

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Start by recalling the relationship between the energy of a photon and its wavelength, which is given by the equation: \( E = \frac{hc}{\lambda} \), where \( E \) is the energy of the photon, \( h \) 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.
Rearrange the equation to solve for wavelength \( \lambda \): \( \lambda = \frac{hc}{E} \).
Substitute the known values into the equation: \( h = 6.626 \times 10^{-34} \) J·s, \( c = 3.00 \times 10^8 \) m/s, and \( E = 6.06 \times 10^{-19} \) J.
Calculate the numerator \( hc \) by multiplying Planck's constant \( h \) by the speed of light \( c \).
Divide the result from the previous step by the energy \( E \) to find the wavelength \( \lambda \).

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Key Concepts

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

Photon Energy

Photon energy is the energy carried by a single photon, which is a particle of light. It is directly proportional to the frequency of the radiation and inversely proportional to its wavelength. The energy of a photon can be calculated using the equation E = hν, where E is energy, h is Planck's constant (6.626 × 10^-34 J·s), and ν is the frequency of the radiation.
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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 × 10^8 m/s), λ is the wavelength, and ν is the frequency. This equation shows that as the wavelength increases, the frequency decreases, and vice versa. Understanding this relationship is crucial for converting between energy, wavelength, and frequency.
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Planck's Constant

Planck's constant is a fundamental constant in quantum mechanics, denoted as h, with a value of approximately 6.626 × 10^-34 J·s. It relates the energy of a photon to its frequency, serving as a bridge between the macroscopic and quantum worlds. This constant is essential for calculations involving photon energy and is a key component in the equations used to solve problems related to electromagnetic radiation.
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Related Practice
Textbook Question
Einstein's 1905 paper on the photoelectric effect was thefirst important application of Planck's quantum hypothesis.Describe Planck's original hypothesis, and explain howEinstein made use of it in his theory of the photoelectriceffect.
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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

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

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Textbook Question

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

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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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