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Ch.8 - The Quantum-Mechanical Model of the Atom
Tro - Chemistry: A Molecular Approach 6th Edition
Tro6th EditionChemistry: A Molecular ApproachISBN: 9780137832217Not the one you use?Change textbook
All textbooksTro 6th EditionCh.8 - The Quantum-Mechanical Model of the AtomProblem 44
Chapter 8, Problem 44

Calculate the energy of a photon of each frequency and state what part of the electromagnetic spectrum is associated with the frequency.
a. 15.77×1017 Hz
b. 1.18×1014 Hz
c. 3.00×1020 Hz

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1
insert step 1: Use the formula for the energy of a photon, which is E = h \(\cdot\) f, where E is the energy, h is Planck's constant (6.626 \(\times\) 10^{-34} \(\text{ J}\[\cdot\]\text{s}\)), and f is the frequency.
insert step 2: For each frequency given, substitute the value of the frequency into the formula.
insert step 3: Calculate the energy for each frequency using the formula.
insert step 4: Identify the part of the electromagnetic spectrum each frequency corresponds to by comparing the frequency to known ranges for radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.
insert step 5: State the energy calculated and the corresponding part of the electromagnetic spectrum for each frequency.

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Key Concepts

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

Photon Energy Calculation

The energy of a photon can be calculated using the formula E = hν, where E is the energy, h is Planck's constant (6.626 × 10^-34 J·s), and ν (nu) is the frequency of the photon. This relationship shows that higher frequency photons have greater energy, which is crucial for understanding the behavior of electromagnetic radiation.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, arranged by frequency or wavelength. Different regions of the spectrum, such as radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays, correspond to specific frequency ranges, influencing their applications and interactions with matter.

Frequency and Wavelength Relationship

Frequency (ν) and wavelength (λ) are inversely related through the equation c = λν, where c is the speed of light (approximately 3.00 × 10^8 m/s). This relationship indicates that as the frequency of electromagnetic radiation increases, its wavelength decreases, which is essential for identifying the part of the spectrum associated with a given frequency.
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Textbook Question

A heat lamp produces 17.7 watts of power at a wavelength of 6.5 μm. How many photons are emitted per second? (1 watt = 1 J/s)

Textbook Question

List these types of electromagnetic radiation in order of (ii) increasing energy per photon.

a. visible light

b. radio waves

c. X-ray

d. ultraviolet radiation

Textbook Question

A laser pulse with wavelength 532 nm contains 1.85 mJ of energy. How many photons are in the laser pulse?

Textbook Question

Calculate the energy of a photon of each wavelength and state what part of the electromagnetic spectrum is associated with the wavelength.

a. 105 nm

b. 715 nm

c. 2.52 cm

Textbook Question

Determine the energy of 1 mol of photons for each kind of light. (Assume three significant figures.) a. infrared radiation (1500 nm) b. visible light (500 nm) c. ultraviolet radiation (150 nm)

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Textbook Question

List these types of electromagnetic radiation in order of (i) increasing frequency and (ii) decreasing energy per photon.

a. gamma rays

b. ultraviolet radiation

c. infrared radiation

d. microwaves