Ch.7 - Quantum MechanicsSee all chapters
All Chapters
Ch.1 - Intro to General Chemistry
Ch.2 - Atoms & Elements
Ch.3 - Chemical Reactions
BONUS: Lab Techniques and Procedures
BONUS: Mathematical Operations and Functions
Ch.4 - Chemical Quantities & Aqueous Reactions
Ch.5 - Gases
Ch.6 - Thermochemistry
Ch.7 - Quantum Mechanics
Ch.8 - Periodic Properties of the Elements
Ch.9 - Bonding & Molecular Structure
Ch.10 - Molecular Shapes & Valence Bond Theory
Ch.11 - Liquids, Solids & Intermolecular Forces
Ch.12 - Solutions
Ch.13 - Chemical Kinetics
Ch.14 - Chemical Equilibrium
Ch.15 - Acid and Base Equilibrium
Ch.16 - Aqueous Equilibrium
Ch. 17 - Chemical Thermodynamics
Ch.18 - Electrochemistry
Ch.19 - Nuclear Chemistry
Ch.20 - Organic Chemistry
Ch.22 - Chemistry of the Nonmetals
Ch.23 - Transition Metals and Coordination Compounds
Light as Particles

Concept #1: Particle Nature of Light Intro

Example #1: Particle Nature of Light

Practice: Rank the following in terms of decreasing energy: Gamma energy, visible light 1 (ΔE = 4.39 x 10-19 J), microwave and visible light 2 (λ = 595 nm).

Additional Problems
You may want to reference (Pages 556 - 557) Section 12.8 while completing this problem.Which wavelength of light (in nanometers) is emitted if an electron moves from the conduction band to the valence band in a sample of diamond? (Note that diamond has a band gap of 5.5 eV .)
A popular kitchen appliance produces electromagnetic radiation with a frequency of 2450 MHz. With reference to the figure below , answer the following:Do photons of this radiation have more or less energy than photons of visible light?
You may want to reference (Pages 299 - 308) Section 7.2 while completing this problem.A 100-watt lightbulb radiates energy at a rate of 100 J/s. (The watt, a unit of power, or energy over time, is defined as 1 J/s.) If all of the light emitted has a wavelength of 530nm, how many photons are emitted per second? (Assume three significant figures in this calculation.)
What is a photon?
One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 320 nm .How many photons are in a 1.15 mJ burst of this radiation?
A diode laser emits at a wavelength of 988 nm .All of its output energy is absorbed in a detector that measures a total energy of 0.53 J over a period of 33 s . How many photons per second are being emitted by the laser?
A laser pulse with wavelength 535 nm contains 4.85 mJ of energy.How many photons are in the laser pulse?
The watt is the derived SI unit of power, the measure of energy per unit time: 1W = 1J/s. A semiconductor laser in a CD player has an output wavelength of 780 nm and a power level of 0.10 mW.How many photons strike the CD surface during the playing of a CD 69 minutes in length?
Microwave ovens use microwave radiation to heat food. The microwaves are absorbed by moisture in the food, which is transferred to other components of the food. As the water becomes hotter, so does the food. Suppose that the microwave radiation has a wavelength of 11.2 cm.How many photons are required to heat 200 mL of coffee from 24 oC to 63 oC?
The human retina has three types of receptor cones, each sensitive to a different range of wavelengths of visible light, as shown in this figure (the colors are merely to differentiate the three curves from one another; they do not indicate the actual colors represented by each curve): Estimate the energies of photons with wavelengths at the maximum for each type of cone.
Carotenoids are yellow, orange, and red pigments synthesized by plants. The observed color of an object is not the color of light it absorbs but rather the complementary color, as described by a color wheel such as the one shown here. On this wheel, complementary colors are across from each other. If a particular carotenoid absorbs photons at 456 nm , what is the energy of the photon?
The energy from radiation can be used to cause the rupture of chemical bonds. A minimum energy of 242 kJ/mol is required to break the chlorine–chlorine bond in Cl2. You may want to reference (Pages 217 - 218) Section 6.2 while completing this problem.What is the longest wavelength of radiation that possesses the necessary energy to break the bond?
Does a photon of red light with a frequency of 4.57 1014 Hz have sufficient energy to promote an electron from the valence band to the conduction band in a sample of silicon (the band gap in silicon is 1.11 eV)?
The energy from radiation can be used to cause the rupture of chemical bonds. A minimum energy of 242 kJ/mol is required to break the chlorine–chlorine bond in Cl2. You may want to reference (Pages 217 - 218) Section 6.2 while completing this problem.What type of electromagnetic radiation is this?
Which wavelength of light (in nm) is emitted if an electron moves from the conduction band to the valence band in a sample of diamond (diamond has a band gap of 5.5 eV)?
Titanium metal requires a photon with a minimum energy of  6.94 10 - 19 to emit electrons. You may want to reference (Pages 217 - 218) Section 6.2 while completing this problem.What is the wavelength of this light?
Calculate the energy of a photon of electromagnetic radiation whose frequency is 2.86×1014 s-1 .
Calculate the energy of a photon of radiation whose wavelength is 421 nm .
What wavelength of radiation has photons of energy 6.26×10−19 J ?
You may want to reference (Pages 299 - 308)section 7.2 while completing this problem. Calculate the energy of a photon of electromagnetic radiation at each of the following frequencies.102.6 MHz (typical frequency for FM radio broadcasting)
You may want to reference (Pages 299 - 308)section 7.2 while completing this problem. Calculate the energy of a photon of electromagnetic radiation at each of the following frequencies.1055 kHz (typical frequency for AM radio broadcasting)
You may want to reference (Pages 299 - 308)section 7.2 while completing this problem. Calculate the energy of a photon of electromagnetic radiation at each of the following frequencies.835.1 MHz (common frequency used for cell phone communication)
One way to measure ionization energies is photoelectron spectroscopy (PES), a technique based on the photoelectric effect. In PES, monochromatic light is directed onto a sample, causing electrons to be emitted. The kinetic energy of the emitted electrons is measured. The difference between the energy of the photons and the kinetic energy of the electrons corresponds to the energy needed to remove the electrons (that is, the ionization energy). Suppose that a PES experiment is performed in which mercury vapor is irradiated with ultraviolet light of wavelength 58.4 nm. What is the energy of a photon of this light, in eV?
Ultraviolet radiation and radiation of shorter wavelengths can damage biological molecules because these kinds of radiation carry enough energy to break bonds within the molecules. A typical carbon-carbon bond requires 348 kJ/mol to break.What is the longest wavelength of radiation with enough energy to break carbon-carbon bonds?
The iodine molecule can be photodissociated (broken apart with light) into iodine atoms in the gas phase with light of wavelengths shorter than about 792 nm. A 130.0 mL glass tube contains 50.1 mtorr of gaseous iodine at 23.0 oC.What minimum amount of light energy must be absorbed by the iodine in the tube to dissociate 16.0 % of the molecules?
What is the value of E in the figure below that would correspond to the absorption of a photon of radiation with frequency 465 MHz ?
How is the energy of a photon related to its wavelength?
How is the energy of a photon related to its frequency?
Calculate the energy of a photon of wavelength 3.4 m .
Calculate the energy of a photon of wavelength 0.154 nm .
Compare the energy of a photon of wavelength 3.4 m with that of wavelength 0.154 nm .
An AM radio station broadcasts at 1030 kHz , and its FM partner broadcasts at 98.4 MHz .Calculate the energy of the photons emitted by the AM radio station.
An AM radio station broadcasts at 1030 kHz , and its FM partner broadcasts at 98.4 MHz .Calculate the energy of the photons emitted by the FM radio station.
One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 320 nm .What is the energy of a photon of this wavelength?
One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 320 nm .These UV photons can break chemical bonds in your skin to cause sunburn—a form of radiation damage. If the 320 nm radiation provides exactly the energy to break an average chemical bond in the skin, estimate the average energy of these bonds in kJ/mol.
A stellar object is emitting radiation at 3.60 mm. You may want to reference (Pages 217 - 218) Section 6.2 while completing this problem.If the detector is capturing 3.3×108 photons per second at this wavelength, what is the total energy of the photons detected in one hour?
Molybdenum metal must absorb radiation with a minimum frequency of 1.09 1015 s - 1 before it can emit an electron from its surface via the photoelectric effect.If molybdenum is irradiated with light of wavelength of 120 nm, what is the maximum possible kinetic energy of the emitted electrons?
If you put 120 volts of electricity through a pickle, the pickle will smoke and start glowing orange-yellow. The light is emitted because sodium ions in the pickle become excited; their return to the ground state results in light emission.What is the energy of 0.10 mol of these photons?
The rays of the Sun that cause tanning and burning are in the ultraviolet portion of the electromagnetic spectrum. These rays are categorized by wavelength: So-called UV-A radiation has wavelengths in the range of 320-380 nm, whereas UV-B radiation has wavelengths in the range of 290-320 nm.Calculate the energy of a mole of 340 - nm photons.
The rays of the Sun that cause tanning and burning are in the ultraviolet portion of the electromagnetic spectrum. These rays are categorized by wavelength: So-called UV-A radiation has wavelengths in the range of 320-380 nm, whereas UV-B radiation has wavelengths in the range of 290-320 nm.Which are more energetic, photons of UV-A radiation or photons of UV-B radiation?
In a future hydrogen-fuel economy, the cheapest source of H 2 will certainly be water. It takes 467 kJ to produce 1 mol of H atoms from water. What is the frequency, wavelength, and minimum energy of a photon that can free an H atom from water?
The optic nerve needs a minimum of 2.0 x 10−17 J of energy to trigger a series of impulses that eventually reach the brain. How many photons of red light (700. nm) are needed?
You may want to reference (Pages 299 - 308) Section 7.2 while completing this problem.A heat lamp produces 24.0 watts of power at a wavelength of 6.4 m. How many photons are emitted per second? (1 W = 1 J/s)
The optic nerve needs a minimum of 2.0 x 10−17 J of energy to trigger a series of impulses that eventually reach the brain. How many photons of blue light (475 nm) are needed?
An argon ion laser puts out 5.1 W of continuous power at a wavelength of 532 nm. The diameter of the laser beam is 5.8 mm. If the laser is pointed toward a pinhole with a diameter of 1.2 mm, how many photons travel through the pinhole per second? Assume that the light intensity is equally distributed throughout the entire cross-sectional area of the beam. (1 W = 1 J/s)
The quantum yield of light-induced chemical reactions (called photochemical reactions) measures the efficiency of the process. The quantum yield, φ, is defined as: φ = (number of reaction events)/(number of photons involved). Suppose a quantum yield for the reaction CH3X → CH3 + X is φ = 0.56. A cuvette containing a solution of CH3X is irradiated with 280-nm light m nm with a power of 885 mW  m mW for 10.0 minutes. Assuming total absorption of the light by the sample, what is the maximum amount (in moles) of CH3X that breaks apart?
A student is studying the photodissociation (dissociation with light) of I2 → 2 I. When a sample of I2 is irradiated with a power of 266 mW at 590 nm for 41 seconds, 0.0256 mmol of I forms. Assuming complete absorption of the incident radiation, what is the quantum yield, φ, of the reaction?
Enormous numbers of microwave photons are needed to warm macroscopic samples of matter. A portion of soup containing 252 g of water is heated in a microwave oven from 20. °C to 98 °C, with radiation of wavelength 1.55 x 10−2 m. How many photons are absorbed by the water in the soup?
Photons of infrared radiation are responsible for much of the warmth we feel when holding our hands before a fire. These photons will also warm other objects. How many infrared photons with a wavelength of 1.5 × 10−6 m must be absorbed by the water to warm a cup of water (175 g) from 25.0 °C to 40 °C?
The eyes of certain reptiles pass a single visual signal to the brain when the visual receptors are struck by photons of a wavelength of 850 nm. If a total energy of 3.15 × 10−14 J is required to trip the signal, what is the minimum number of photons that must strike the receptor?
A Blu-ray laser has a power of 5 milliwatts (1 watt = 1 J s−1). How many photons of light are produced by the laser in 1 hour?
Carbon absorbs energy at a wavelength of 150. nm. The total amount of energy emitted by a carbon sample is 1.98 x 105 J. Calculate the number of carbon atoms present in the sample, assuming that each atom emits one photon.
Electric power is measured in watts (1 W = 1 J/s). About 95% of the power output of an incandescent bulb is converted to heat and 5% to light. If 10% of that light shines on your chemistry textbook, how many photons per second shine on the book from a 75-W bulb?(Assume that the photons have a wavelength of 550 nm.)
You may want to reference (Pages 296 - 324) Chapter 7 while completing this problem.A green leaf has a surface area of 2.55 cm2. If solar radiation is 1110 W/m2, how many photons strike the leaf every second? Assume three significant figures and an average wavelength of 504 nm for solar radiation.
A sodium flame has a characteristic yellow color due to emission of light of wavelength 589 nm. What is the mass equivalence of one photon with this wavelength (1 J = 1 kg⋅m2/s2)?
A lithium flame has a characteristic red color due to emission of light of wavelength 671 nm. What is the mass equivalence of 1 mol photons with this wavelength (1 J = 1 kg⋅m2/s2)?
The net change during photosynthesis involves CO2 and H2O forming glucose (C6H12O6) and O2. Chlorophyll absorbs light in the 600–700 nm region. What is the minimum number of photons with λ = 680. nm needed to form 1.00 mol of glucose?
You may want to reference (Pages 296 - 324) Chapter 7 while completing this problem.A 6.00 mL ampule of a 0.130 M solution of naphthalene in hexane is excited with a flash of light. The naphthalene emits 15.0 J of energy at an average wavelength of 349 nm. What percentage of the naphthalene molecules emitted a photon?
Water is exposed to infrared radiation of wavelength 2.8×10−4 cm. Assume that all the radiation is absorbed and converted to heat. How many photons will be required to raise the temperature of 2.1 g of water by 2.2 K?
The heat of fusion of ice is 6.00 kJ/mol. Find the number of photons of wavelength λ = 6.01×10−6 m that must be absorbed to melt 5.50 g of ice.
You may want to reference (Pages 296 - 324) Chapter 7 while completing this problem.The human eye contains a molecule called 11-cis-retinal that changes shape when struck with light of sufficient energy. The change in shape triggers a series of events that results in an electrical signal being sent to the brain that results in vision. The minimum energy required to change the conformation of 11-cis-retinal within the eye is about 164 kJ/mol. Calculate the longest wavelength visible to the human eye.
You may want to reference (Pages 299 - 308) section 7.2 while completing this problem.How much energy is contained in 1 mol of X-ray photons with a wavelength of 0.135 nm.
You may want to reference (Pages 299 - 308) section 7.2 while completing this problem.How much energy is contained in 1 mol of γ-ray photons with a wavelength of 2.56×10−5 nm{ m nm}.
A bright violet line occurs at 435.8 nm in the emission spectrum of mercury vapor. What amount of energy, in joules, must be released by an electron in a mercury atom to produce a photon of this light?
Cesium was discovered in natural mineral waters in 1860 by R. W. Bunsen and G. R. Kirchhoff, using the spectroscope they invented in 1859. The name came from the Latin caesius (“sky blue”) because of the prominent blue line observed for this element at 455.5 nm. Calculate the frequency and energy of a photon of this light.
The bright yellow light emitted by a sodium vapor lamp consists of two emission lines at 589.0 and 589.6 nm. What are the frequency and the energy of a photon of light at each of these wavelengths? What are the energies in kJ/mol?
Light with a wavelength of 614.5 nm looks orange. What is the energy, in joules, per photon of this orange light? What is the energy in eV (1 eV = 1.602 × 10−19 J)?
A laser (light amplification by stimulated emission of radiation) provides nearly monochromatic high-intensity light. Lasers are used in eye surgery, CD/DVD players, basic research, and many other areas. Some dye lasers can be “tuned” to emit a desired wavelength. Fill in the blanks in the following table of the properties of some common types of lasers:
Heated lithium atoms emit photons of light with an energy of 2.961 × 10−19 J. Calculate the frequency and wavelength of one of these photons. What is the total energy in 1 mole of these photons? What is the color of the emitted light?
A photon of light produced by a surgical laser has an energy of 3.027 × 10−19 J. Calculate the frequency and wavelength of the photon. What is the total energy in 1 mole of photons? What is the color of the emitted light?
The emission spectrum of cesium contain this line whose frequency is 3.45 × 10 14 Hz. What is the wavelength and energy per photon of the line? What color is the line?
The energy difference between the 5d and 6s sublevels in gold accounts for its color. Assuming this energy difference is about 2.7 eV (electron volts; 1 eV = 1.602 x 10−19 J), explain why gold has a warm yellow color.
The emission spectrum of cesium contain this line whose frequency is 6.53 × 10 14 Hz. What is the wavelength and energy per photon of the line? What color is the line?
A carbon–oxygen double bond in a certain organic molecule absorbs radiation that has a frequency of 6.0 x 1013 s-1. What is the energy of this radiation per photon?
Does the following equation describe particle-like or wavelike behavior? Does it involve both types of behavior?(b) E = mν2/2
One of the radiographic devices used in a dentist's office emits an X-ray of wavelength 2.090 × 10−11 m. What is the energy, in joules, and frequency of this X-ray?
Does the following equation describe particle-like or wavelike behavior? Does it involve both types of behavior?(d) E = hν
Consider the following approximate visible light spectrum:Barium emits light in the visible region of the spectrum. If each photon of light emitted from barium has an energy of 3.59 x 10-19 J, what color of visible light is emitted?
RGB color television and computer displays use cathode ray tubes that produce colors by mixing red, green, and blue light. If we look at the screen with a magnifying glass, we can see individual dots turn on and off as the colors change. Using a spectrum of visible light, determine the approximate wavelength of each of these colors. What is the frequency and energy of a photon of each of these colors?
Microwave radiation has a wavelength on the order of 1.0 cm. Calculate the frequency and the energy of a single photon of this radiation.
A photon of ultraviolet (UV) light possesses enough energy to mutate a strand of human DNA. What is the energy of a single UV photon and 1 mole of UV photons having a wavelength of 25 nm? 1 mol UV photons = 6.022 x 1023 UV photons.
The following values are the only energy levels of a hypothetical one-electron atom:E6 = −2 x 10−19 J               E  5 = −7 x 10−19 JE4 = −11 x 10−19 J               E  3 = −15 x 10−19 JE2 = −17 x 10−19 J               E  1 = −20 x 10−19 JIf the electron were in the  n = 3 level, what would be the highest frequency (and minimum wavelength) of radiation that could be emitted?
The following values are the only energy levels of a hypothetical one-electron atom:E6 = −2 x 10−19 J               E  5 = −7 x 10−19 JE4 = −11 x 10−19 J               E  3 = −15 x 10−19 JE2 = −17 x 10−19 J               E  1 = −20 x 10−19 JIf the electron were in the  n = 4 level, what would be the shortest wavelength (in nm) of radiation that could be absorbed without causing ionization?
Photoelectron spectroscopy applies the principle of the photoelectric effect to study orbital energies of atoms and molecules. High-energy radiation (usually UV or x-ray) is absorbed by a sample and an electron is ejected. The orbital energy can be calculated from the known energy of the radiation and the measured energy of the electron lost. The following energy differences were determined for several electron transitions:ΔE2⟶1 = 4.098 x 10−17 J               ΔE  3⟶1 = 4.854 x 10−17 JΔE5⟶1 = 5.242 x 10−17 J               ΔE  4⟶2 = 1.024 x 10−17 JCalculate ΔE and λ of a photon emitted in the transitions level 4 → 1.
Photoelectron spectroscopy applies the principle of the photoelectric effect to study orbital energies of atoms and molecules. High-energy radiation (usually UV or x-ray) is absorbed by a sample and an electron is ejected. The orbital energy can be calculated from the known energy of the radiation and the measured energy of the electron lost. The following energy differences were determined for several electron transitions:ΔE2⟶1 = 4.098 x 10−17 J               ΔE  3⟶1 = 4.854 x 10−17 JΔE5⟶1 = 5.242 x 10−17 J               ΔE  4⟶2 = 1.024 x 10−17 JCalculate ΔE and λ of a photon emitted in the transitions level 5 → 4.
Consider the following waves representing electromagnetic radiation:Which wave has the longer wavelength? Calculate the wavelength. Which wave has the higher frequency and larger photon energy? Calculate these values. Which wave has the greater velocity? What type of electromagnetic radiation does each wave represent?
A radio wave has a frequency of 3.8 x 10 10 Hz. What is the energy (in J) of one photon of this radiation?
An x-ray has a wavelength of 1.3 Å. Calculate the energy (in J) of one photon of this radiation.
X rays have wavelengths on the order of 1 x 10-10 m. Calculate the energy of 1.0 x 10 -10 m X rays in units of kilojoules per mole of X rays. (1 mol X rays = 6.022 x 10  23 X rays). AM radio waves have wavelengths on the order of 1 x 10 4 m. Calculate the energy of 1.0 x 10 4 m radio waves in units of kilojoules per mole of radio waves. Consider that the bond energy of a carbon–carbon single bond found in organic compounds is 347 kJ/mol. Would X rays and/or radio waves be able to disrupt organic compounds by breaking carbon–carbon single bonds?
You may want to reference (Pages 299 - 308) Section 7.2 while completing this problem.Calculate the energy of a photon of electromagnetic radiation at each of the following wavelengths.632.8 nm (wavelength of red light from a helium-neon laser)
You may want to reference (Pages 299 - 308) Section 7.2 while completing this problem.Calculate the energy of a photon of electromagnetic radiation at each of the following wavelengths.503 nm (wavelength of maximum solar radiation)
You may want to reference (Pages 299 - 308) Section 7.2 while completing this problem.Calculate the energy of a photon of electromagnetic radiation at each of the following wavelengths.0.0520 nm (a wavelength used in medical X rays)
You may want to reference (Pages 299 - 308) Section 7.2 while completing this problem.Determine the energy of 1.60 mol of photons for each of the following kinds of light. (Assume three significant figures.)infrared radiation (1510 nm)
You may want to reference (Pages 299 - 308) Section 7.2 while completing this problem.Determine the energy of 1.60 mol of photons for each of the following kinds of light. (Assume three significant figures.)visible light (505 nm)
You may want to reference (Pages 299 - 308) Section 7.2 while completing this problem.Determine the energy of 1.60 mol of photons for each of the following kinds of light. (Assume three significant figures.)ultraviolet radiation (155 nm)
Cobalt-60 is a radioactive isotope used to treat cancers. A gamma ray emitted by this isotope has an energy of 1.33 MeV (million electron volts; 1 eV = 1.602 x 10−19 J). What is the frequency (in Hz) and the wavelength (in m) of this gamma ray?
Ozone formation in the upper atmosphere starts when oxygen molecules absorb UV radiation with wavelengths less than or equal to 242 nm. Find the frequency and energy of the least energetic of these photons.
Ozone absorbs radiation with wavelengths in the range 2200–2900 Å, thus protecting organisms from this radiation. Find the frequency and energy of the most energetic of these photons.
In addition to continuous radiation, fluorescent lamps emit some visible lines from mercury. A prominent line has a wavelength of 436 nm. What is the energy (in J) of one photon of it?
Photogray lenses incorporate small amounts of silver chloride in the glass of the lens. When light hits the AgCl particles, the following reaction occurs:The silver metal that is formed causes the lenses to darken. The energy change for this reaction is 3.10 x 102 kJ/mol. Assuming all this energy must be supplied by light, what is the maximum wavelength of light that can cause this reaction?
A laser produces 21.0 mW of light. In 3.00 hr, the laser emits 4.53×1020 photons. What is the wavelength of the laser?
A particular laser consumes 160.0 Watts of electrical power and produces a stream of 2.51×1019 1121-nm photons per second. What is the percent efficiency of the laser in converting electrical power to light?
You may want to reference (Page 305) Section 7.2 while completing this problem.How much energy (in J) is contained in 1.00 mole of 601-nm photons?
A photon has a wavelength of 759 nm. Calculate the energy of the photon in joules. Enter your answer in scientific notation. 
A certain shade of blue has a frequency of 7.01 x1014 Hz. What is the energy of exactly one photon of this ight?
Be sure answer all parts.How many photons at 586 nm must be absorbed to melt 5.15 x 102 g of ice? (It takes 334 J to melt 1 g of ice at 0°C.) (Enter your answer in scientific notation.) On average, how many H2O molecules does one photon convert from ice to water? (Enter your answer in scientific notation.)