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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: 9780137832217Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoTro 6th EditionCh.8 - The Quantum-Mechanical Model of the AtomProblema 43
Capitolo 8, Problema 43

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

Guida verificata passo dopo passo
1
insert step 1: Understand the relationship between energy and wavelength using the formula: E = \(\frac{hc}{\lambda}\), where E is the energy of the photon, h is Planck's constant (6.626 \(\times\) 10^{-34} \(\text{ J s}\)), c is the speed of light (3.00 \(\times\) 10^8 \(\text{ m/s}\)), and \(\lambda\) is the wavelength.
insert step 2: Convert the given wavelengths into meters for consistency in units. For example, 105 nm = 105 \(\times\) 10^{-9} m, 715 nm = 715 \(\times\) 10^{-9} m, and 2.52 cm = 2.52 \(\times\) 10^{-2} m.
insert step 3: Substitute the converted wavelength values into the energy formula for each case to calculate the energy of the photon.
insert step 4: Identify the part of the electromagnetic spectrum each wavelength corresponds to. For instance, 105 nm is in the ultraviolet range, 715 nm is in the visible range (red light), and 2.52 cm is in the microwave range.
insert step 5: Summarize the findings by stating the energy calculated for each wavelength and the corresponding part of the electromagnetic spectrum.

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Photon Energy Calculation

The energy of a photon can be calculated using the equation E = hc/λ, where E is the energy, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength in meters. This relationship shows that energy is inversely proportional to wavelength; shorter wavelengths correspond to higher energy photons.
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Moles and Photon Energy

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, arranged by wavelength or frequency. It includes gamma rays, X-rays, ultraviolet light, visible light, infrared radiation, microwaves, and radio waves. Each region of the spectrum has distinct properties and applications, with visible light being the only part detectable by the human eye.
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Wavelength Conversion

To calculate photon energy accurately, wavelengths must be in meters. For example, to convert nanometers (nm) to meters, divide by 1 billion (1 nm = 1 x 10^-9 m), and for centimeters (cm), divide by 100 (1 cm = 0.01 m). This conversion is essential for applying the photon energy formula correctly and identifying the corresponding part of the electromagnetic spectrum.
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Conversion Factors
Pratica correlata
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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)

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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

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

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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

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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

Domanda del libro di testo

Calculate the frequency of each wavelength of electromagnetic radiation: a. 632.8 nm (wavelength of red light from helium–neon laser) b. 503 nm (wavelength of maximum solar radiation) c. 0.052 nm (wavelength contained in medical X-rays)

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