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

Wavelength is the distance from one crest of a wave to another, whereas frequency is the number of waves within a second. 

The Electromagnetic Spectrum

The electromagnetic spectrum consists of varying forms of energy within oscillating electric and magnetic fields. 

Concept #1: The Electromagnetic Spectrum

Concept #2: Wavelength & Frequency

Concept #3: The relationship between Wavelength & Frequency

Wavelength and Frequency are inversely proportional, meaning that if one increases then the other one must decrease. 

Practice: A. Based on the images of different electromagnetic waves, answer each of the following questions.

a) Which electromagnetic wave has the longest wavelength?

b) Which electromagnetic wave has the greatest energy?

c) Which electromagnetic wave has the lowest frequency?

d) Which electromagnetic wave has the largest amplitude?


Wavelength & Frequency Calculations

Concept #4: Converting between Wavelength and   Frequency

To convert between wavelength & frequency we use the equation c = ν  λ, where c equals the speed of light. 

Example #1: Even the music we listen to deals with how energy travels to get to our car radio. If Power 96 broadcasts its music at 96.5 MHz (megahertz, or 106 Hertz) find the wavelength in micrometers and Angstroms of the radio waves.  

Practice: Calculate the frequency of the red light emitted by a neon sign with a wavelength of 663.8 nm.

Additional Problems
The speed of light in air 1. is independent of the wavelength and frequency of light. 2. depends on both the wavelength and the frequency of light. 3. depends only on the wavelength of light. 4. depends only on the frequency of the light.
A low-pressure mercury-vapor lamp has a characteristic emission line at 253 nm. Knowing that this lamp is putting out 11.8 watts of light energy, how many mercury atoms are emitted per second during operation? 1. 5.25 x 1020 atoms 2. 7.11 x 1024 atoms 3. 1.50 x 1019 atoms  4. 1.08 x 1017 atoms 5. 7.86 x 10−19 atoms 6. 4.73 x 105 atoms
The binding energy of an electron in iron is 7.49 × 10 –19 J. What is the maximum wavelength of light that can be used to eject electrons from iron? A) 265 nm B) 636 nm C) 542 nm D) 339 nm E) 800 nm
For light with a wavelength of 12.5 nm, determine the energy of light in kJ/mol. A. 4.99 * 10−18 B. 0.00957 C. 4.99 D. 9.57 E. 9570
Determine the wavelength (in nm) of an X-ray with a frequency of 4.2 × 10 18Hz. a. 7.1 × 10 –11 b. 7.1 × 10 –2 c. 1.3 × 10 27 d. 1.4 × 10 10 e. 7.1 × 10 –18
The wavelength of light with a frequency of 3.30 × 10 14 s −1 is 1. 450 nm. 2. 909 nm. 3. 200 nm. 4. 650 nm.
Calculate the energy in kJ/mol of light with a wavelength of 360 nm. A) 332 kJ/mol B) 5.52 × 10-19 kJ/mol C) 0.332 kJ/mol D) 5.52 × 10-22 kJ/mol E) 6.63 × 103 kJ/mol  
What is the wavelength of a particle that has an energy of 4.41 × 10 –19 J?   a) 441 nm b) 450 nm c) 227 nm d) 222 nm e) 199 nm
How many photons of light with frequency 5.50 × 10 15 Hz are required to provide 1 kJ of energy? A) 2.74 × 1020 photons B) 3.64 × 10-16 photons C) 3.64 × 10-18 photons D) 4.56 × 10-4 photons E) 1.65 × 1044 photons  
What is the frequency (Hz) of an infrared light that emits 24.5 kJ/mol of energy? a) 3.70 × 10 34 b) 6.14 × 10 13 c) 4.92 × 10 19 d) 8.17 × 10 –8 e) 2.70 × 10 –35
Ultraviolet light emits a total of 2.5 × 10 –17 J of light at a wavelength of 9.8 × 10 –7 m. How many photons does this correspond to? a) 1 b) 10 c) 25 d) 100 e) 125
What is the energy in joules of a mole of photons with the energy of the 434 nm spectral line of hydrogen? A) 5.78 × 10-25 J B) 2.76 × 10-4 J C) 434 J D) 9.21 × 10-4 J E) 2.76 × 105 J  
What is the frequency of a 534 nm photon? 1. 6.04e+14 2. 5.56e+14 3. 6.98e+14 4. 4.29e+14 5. 5.21e+14 6. 4.76e+14 7. 5.8e+14 8. 4.17e+14 9. 4.91e+14 10. 5.62+14
Electromagnetic radiation with a wavelength of 525 nm appears as green light to the human eye. The energy of one photon of this light is __________ J.   A) 3.79 ×10-28 B) 2.64 ×1018 C) 1.04 × 10-22 D) 1.04 × 10-31 E) 3.79 ×10-19
Slightly more than of the total energy from the Sun is infrared, which has a critical effect on the earth's climate. The wavelength of this infrared light is about 4.00 x 10-6 m. What is the frequency of the infrared light described above? A) 7.5 x 1013 Hz B) 6.0 x 1013 Hz C) 1.7 x 10-14 Hz D) 2.0 x 105 Hz What is the energy of the infrared light described above? A) 9.9 x 10-31 J B) 5.0 x 10-20 J C) 1.1 x 10-47 J D) 1.3 x 10-28 J
It takes light with a wavelength of 212 nm to break the NH bond in ammonia. What energy is required and what is the NH bond strength? 1. 6.6×10−22 kJ/photon, 4 × 10−4 kJ/mol 2. 9.4 × 10−19 kJ/photon, 565 kJ/mol 3. 9.4 × 10−22 kJ/photon, 565 kJ/mol  4. 6.6 × 10−22 kJ/photon, 0.40 kJ/mol 5. 9.4 × 10−22 kJ/photon, 565,000 kJ/mol
You have measured the energy of a photon that you captured in a specialized detector, and found that the photon had an energy of 6.89 × 10 −24 J. Based on the scale below, what type of photon was detected? (a) Gamma(γ) ray (b) X ray (c) Ultraviolet (UV)/Visible (d) Infrared (IR) (e) Microwave                
What is the energy (in kJ/mol) of red photons with a frequency equal to 4.00 x 10  14 Hz? A. 5.30 x 102 B. 1.60 x 102 C. 480 x 102 D. 480 x 103  E. 5.30 x 103
Blu-ray DVDs are read with a laser that has a wavelength of 405 nm. Calculate the energy of one mole of photons from this type of laser.           (a) 345 kJ          (b) 2.96×10 5 J          (c) 3.38×10 −6 J          (d) 4.91×10 −19 J          (e) 4.73×10 4 J
One type of ultraviolet light has a wavelength of 223 nm. Calculate the energy of one photon of this light. a. 8.91 x 10 -19 J b. 6.95 x 10 -19 J c. 7.12 x 10 -19 J d. 7. 87 x 10 -19 J
Ham radio operators often broadcast on the 6-meter band. The frequency of this electromagnetic radiation is __________ MHz. a) 50 b) 20 c) 2.0 d) 200 e) 500
A mixture of argon and mercury vapor used in advertising signs emits light of wavelength 560 nm. Calculate the energy change resulting from the emission of 1.00 mol of photons at this wavelength. 1. 272.058 2. 184.162 3. 187.04 4. 213.759 5. 249.386 6. 217.646 7. 299.263 8. 199.509 9. 221,677 10. 225.859  
How many photons are contained in a burst of yellow light (589 nm) from a sodium lamp that contains 609 kJ of energy? A) 3.06 × 1030 photons B) 2.48 × 1025 photons C) 1.81 × 1024 photons D) 3.37 × 1019 photons E) 4.03 × 1028 photons  
What is the frequency of the medical X-ray at 0.052 nm?  
A line in the spectrum of an element was observed to have a frequesncy of 5.17 x 1014 s -1 . What is the wavelength of this radiation? a. 5.80 x 10-7 meters b. 1.72 x 106 meters c. 1.55 x 1023 meters d. 1.77 x 10-4 meters e. 174 meters
It takes 238 kJ/mol to break a carbon-iodine bond. Calculate the frequency of light for which one carbon-iodine bond could be broken by absorbing a single photon. a) 5.03 x 10-7s-1 b) 5.96 x 1011 s-1 c) 3.59 x 1035 s-1 d) 3.59 x 1038 s-1 e) 5.96 x 1014 s-1
Carbon emits photons at 745 nm when exposed to blackbody radiation. How much energy would be obtained if 44g of carbon were irradiated? Assume each carbon atom emits one photon. a. 9.1 x 10 5 J b. 2.7 x 10 -19 J c. 7.1 x 10 6 J d. 5.9 x 10 5 J
How much energy is contained in 2.5 moles of 455 nm photons?
How much energy (in kJ) do 3.0 moles of photons, all with a wavelength of 655 nm, contain? A) 303 kJ B) 394 kJ C) 254 kJ D) 548 kJ E) 183 kJ  
A. Calculate the energy of a photon with a wavelength of 100 nm.         Convert the energy to units of kJ/mol.     Is this photon within the region for visible light, higher in energy, or lower in energy? ________________ B. How would you calculate the speed of hydrogen atom with a wavelength of 1.00 nm? Set up the equation, including conversion factors, but do not do the calculation. 
Calculate the frequency of visible light having a wavelength of 686 nm. A) 4.37 x 1014 /s B) 4.37 x 105 /s C) 2.06 x 102 /s D) 2.29 x 10-15 /s E) 2.29 x 10-6 /s
In 1.0 s, a 60 W bulb emits 11 J of energy in the form of infrared radiation (heat) of wavelength 1850 nm. How many photons of infrared radiation does the lamp generate in 1.0 s? 1. 6.82 x 10 –14 photons 2. 1.04 x 10 29 photons 3. 6.63 x 10 23 photons 4. 1.10 x 10 –19 photons 5. 1.02 x 10 20 photons
An ultraviolet (UV) light photon has a wavelength of 124.1 nm. What is its energy in joules?
Many small appliances and electronics operate in the microwave region. If your television operates at a 21.25 GHz, then what is the wavelength in nm?
A photovoltaic cell converts light into electrical energy. Suppose a certain photovoltaic cell is only 63.5% efficient, in other words, that 63.5% of the light energy is ultimately recovered. If the energy output of this cell is used to heat water, how many 520 nm photons must be absorbed by the photovoltaic cell in order to heat 10.0 g of water from 20.0°C to 30.0°?
Most of the light emitted by excited mercury atoms has wavelengths of 185, 254, 365, 436, 546 and 615 nm. Which one of the following frequencies is emitted by mercury atoms? A) 1.4 x 1014 s-1 B) 4.1 x 1014 s-1 C) 8.2 x 1014 s-1 D) 8.2 x 1015 s-1 E) 4.1 x 1015 s-1
What is the wavelength of a beam of light having a frequency of 6 × 10  17 Hz? 1. 1.8 × 10 21 nm 2. 2 nm 3. 0.5 nm 4. 50 nm
The energy of a photon is 1. nλ. 2. cλ. 3. c/λ . 4. λ/hc . 5. hc/λ .
The carcinogen, CCl4 has been dumped into a holding pond.  CCl4 will begin to decompose by the following reaction: CCl4 →  Cl3C•   +   Cl•              D(C—Cl) = 327 kJ/mol If sunlight striking the earth has a frequency range from approximately 6.7 x 10 14 Hz to 4.4 x 1014  Hz. Can you expect sunlight alone to affect the decomposition?  Explain. h= 6.63 x 10  -34 J•sec; c = 3.00 x 108  m/sec
The carcinogen, CCl4 has been dumped into a holding pond. CCl4 will begin to decompose by the following reaction:      CCl4   → Cl3C•   + Cl•       ΔΕ for C—Cl bond = 327 kJ/mol Sunlight striking the earth has a frequency range from approximately 6.7×10 14 Hz to 4.4×10 14  Hz.If you assume the highest energy light must be the same energy of the Cl-Cl bond, can you expect sunlight alone to effect the decomposition?h = 6.63×10 -34 J•sec; c = 3.00 ×10 8  m/sec  
A laser pulse produces 1.046 kJ of energy. It was experimentally determined that the pulse contains 3.50 x 1022 photons. Determine the wavelength of light (in meters) emitted by one photon. A) 6.65 x 10-3 m B) 1.50 x 105 m C) 5.43 x 10-48 m D) 1.50 x 102 m E) 6.65 x 10-6 m
What is the wavelength of light if the energy of a photon is 3.65 x 10  -19 J? A) 545 nm B) 5.45 x 10-7 nm C) 1.84 x 106 nm D) 5.51 x 1014 nm E) 654 nm
The human eye contains a molecule called 11-cis-retinal that changes conformation when struck with light of sufficient energy. The change in conformation triggers a series of events that results in an electrical signal being sent to the brain. 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.  
The absorption of light of frequency 1.16 × 10 11 Hz is required for CO molecules to go from the lowest rotational energy level to the next highest rotational energy level. Determine the energy for this transition in kJ/mol. h = 6.626 × 10-34 J ∙ s A) 7.69 ×10-23 kJ/mol B) 46.3 kJ/mol C) 949 kJ/mol D) 0.0463 kJ/mol  
Electromagnetic radiation with a wavelength of 525 nm appears as green light to the human eye. The frequency of this light is __________ s-1. A) 1.58 ×1011 B) 5.71 ×105 C) 1.75 ×10-15 D) 5.71 ×1014 E) 1.58 ×102
Which of the following occur as the energy of a photon increases?a. The frequency decreases.b. The speed increases.c. The wavelength increases.d. The wavelength gets shorter.e. None of the above.
Use Planck's equation to determine the energy, in J/photon, of radiation of frequency 5.8 × 1015 s-1. A) 5.8 ×10-25 J B) 1.7 ×10-16 J C) 3.8 ×10-18 J D) 5.2 ×10-8 J E) 1.7 ×1024 J  
How many photons of light with frequency 5.50 x 10 15 Hz are required to provide 1 kJ of energy?A. 1.65 x 10 44 photonsB. 2.74 x 10 20 photonsC. 3.64 x 10 -16 photonsD. 3.64 x 10 -18 photonsE. 4.56 x 10 -4 photons
What is the energy, in joules, of a mole of photons associated with visible light of wavelength 486 nm? A) 2.46 × 10–4 J B) 6.46 × 10–25 J C) 246 kJ D) 6.46 × 10–16 J E) 12.4 kJ
Where h = 6.626 x 10 -34 J s ( Planck's constant ) and c = 2.99 x 10 8 m/s. What is the wavelength of a photon that has an energy of E = 4.13 x 10-19 J? (in meters). The equation for photon energy E is? 
What is the energy in joules of a mole of photons with the energy of the 434 nm spectral line of hydrogen?A) 5.78 × 10-25 JB) 2.76 × 10-4 JC) 434 JD) 9.21 × 10-4 JE) 2.76 × 105 J
Medical applications of electromagnetic radiation cover the entire spectrum, from gamma rays used to diagnose and treat cancer, to radio waves used in magnetic resonance imaging (MRI). Until recently the tools did not exist to exploit the range from 0.1 to 10 THz, leading some to call this region of the spectrum from 0.1 to 10 THz the “terahertz gap.” But that gap is starting to close as new techniques are developed to explore the terahertz region of the spectrum (Chemistry & Engineering News, 2015, 93, 10-14). It was discovered the terahertz light causes groups of water molecules to coalesce and disassemble repeatedly, and because water permeates most biological studies, terahertz spectroscopy holds considerable promise as important new tool in medical science. A. Calculate the energy (in J) of a 2.4 THz photon.(1 THz = 1 x 1012 Hz = 1 x 1012 s -1 )    Convert your answer above from J to kJ/mol.    B. Calculate the wavelength (in nm) of a 2.4 THz photon.   Do you expect 2.4 THz light to be dangerous to biological tissue? Explain your reasoning. 
Calculate the frequency of each of the following wavelengths of electromagnetic radiation.a. 488.0 nm (wavelength of argon laser)b. 503 nm (wavelength of maximum solar radiation)c. 0.0520 nm (a wavelength contained in medical X-rays)
Green light has a frequency of about 6.00 x 10 14 s-1 . What is the energy of a photon of green light? (4 sig. fig) E = J  
Calculate the frequency of visible light having a wavelength of 486 nm. a. 2.06 x 1014 s-1 b. 2.06 x 106 s-1 c. 6. 17 x 1014 s-1  d. 1.20 x 10-15 s-1  e. 4.86 x 10-7 s-1 
The energy of a photon that has a wavelength of 9.0 m is _____ J. a. 2.2 x 10-26 b. 4.5 x 1025 c. 6.0 x 10-23 d. 2.7 x 109 e. 4.5 x 10-25
Calculate the wavelength (in nm) of the red light emitted by a neon sign with a frequency of 4.74 ×1014 Hz. A) 704 nm B) 158 nm C) 466 nm D) 142 nm E) 633 nm  
Calculate the wavelength (in nm) of the blue light emitted by a mercury lamp with a frequency of 6.88 ×1014 Hz. A) 229 nm B) 206 nm C) 436 nm D) 675 nm E) 485 nm  
Calculate the frequency of the red light emitted by a neon sign with a wavelength of 659.9 nm. A) 4.55 ×1014 s-1 B) 1.98 ×1014 s-1 C) 3.32 ×1014 s-1 D) 5.05 ×1014 s-1 E) 2.20 ×1014 s-1  
Calculate the frequency of the green light emitted by a hydrogen atom with a wavelength of 486.1 nm. A) 6.17 ×1014 s-1 B) 1.46 ×1014 s-1 C) 4.33 ×1014 s-1 D) 1.62 ×1014 s-1 E) 6.86 ×1014 s-1  
How many photons are contained in a flash of green light (525 nm) that contains 189 kJ of energy? (a) 4.99 x 1023 (b) 7.99 x 1030 (c) 5.67 x 1023 (d) 1.25 x 1031 (e) 3.75 x 1023
Calculate the energy of a photon of electromagnetic radiation at each of the following frequencies (in J). i) 103.7 MHz (typical frequency for FM radio broadcasting) ii) 1100 kHz (typical frequency for AM radio broadcasting) (assume four significant figures)
Calculate the energy of the orange light emitted by a neon sign with a frequency of 4.89 × 1014 Hz. A) 5.11 × 10-19 J B) 3.09 × 10-19 J C) 6.14 × 10-19 J D) 1.63 × 10-19 J E) 3.24 × 10-19 J  
Hospital X-ray generators emit X rays with wavelength of about 15.0 nm, where 1 nm = 10 -9 m. What is the energy of a photon in an X ray? Express answer in joules.
My microwave operates at a wavelength of 300.0 mm (note units). What is the energy of a mole of photons generated by this microwave? The value of Planck’s constant, h = 6.63 x 10-34 J s. a. 4.3 kJ b. 4.3 x 10-5 kJ c. 330 kJ d. 4.0 x 10-4 kJ e. 5.5 x 10-25 kJ
How much energy is contained in 1 mol of each of the following? a. X-ray photons with a wavelength of 0.135 nm. Express the energy numerically in kilojoules per mole. b. γ-ray photons with a wavelength of 2.38×10−5 nm. Express the energy numerically in kilojoules per mole.
What is the energy (J) of a photon of a 1 km radio wave? a) 1 x 10-25 b) 1 x 10-28 c) 2 x 10-25 d) 2 x 10-28 e) 5 x 10-25
What is the wavelength (m) of light that has a frequency of 1.20 x 10 13 s-1 a) 2.50 x 10-5 b) 25.0  c) 0.0400  d) 4.00 x 104 e) 2.5
A photon from a indigo laser has a wavelength of 465 nm. What is the energy of a photon from this laser?a. 4.3 x 10-28 Jb. 3.08 x 10-31 Jc. 1.4 x 10-27 Jd. 4.27 x 10-19 Je. 1.79 x 10-18 J
How many photons are contained in a flash of green light (525 nm) that contains 189 kJ of energy?
The wavelength of the red light is 700.5 nm. What is the frequency of red light?
Calculate the energy of a photon of electromagnetic radiation at each of the following frequencies. i) 102.3 mHz (typical frequency for FM radio broadcasting)     ii) 1055 kHz (typical frequency for AM radio broadcasting) (assume four significant figures)     iii) 835.6 MHz (common frequency used for cell phone communication)
A 1.00 mL ampule of a 0.150 M solution of naphthalene in hexane is excited with a flash of light. The naphthalene emits 19.9 J of energy at an average wavelength of 349 nm.What percentage of the naphthalene molecules emitted a photon?
What is the wavelength of yellow light (in nanometers) having a frequency of 5.17 x 1014 s-1? a) 3.84 x 10-31 m b) 5.80 x 10-7 m c) 1.72 x 10-6 m d) 5.80 x 102 m e) 1.72 x 104 m  
What is the energy of a photon of ultraviolet radiation, λ= 500 pm? a) 1.11 x 10-49 J b) 1.67 x 10-16 J c) 9.95 x 10-33 J d) 3.98 x 10-16 J e) 7.24 x 10-12 J
Calculate the frequency (Hz) and energy (J/photon) of visible light with a wavelength of 325nm.
How many photons are produced in a laser pulse of 0.528 J at 679 nm?
The energy of a photon of light is given by E = hv. The frequency, v, of light and the wavelength, λ, are related through: v = c/λ where c is the speed of light, 2.998 x 108 m/s. Arrange the following wavelengths of light from lowest energy to highest energy: 461 nm, 637 nm, 517 nm.  What is the energetic of a photon light with a wavelength of 415 nm?
Calculate the wavelength of each of the following frequencies of electromagnetic radiation. Express your answer using four significant figures.a. 1045 kHz (typical frequency for AM radio broadcasting) (assume four significant figures)b. 835.6 MHz (common frequency used for cell phone communication)
Calculate the energy of a photon of electromagnetic radiation at each of the following frequencies. Express your answer using four significant figures.a. 104.2 MHz (typical frequency for FM radio broadcasting)b. 1070 kHz (typical frequency for AM radio broadcasting) (assume four significant figures)c. 835.6 MHz (common frequency used for cell phone communication)
Ionization involves completely removing an electron from an atom. Light of a particular wavelength can cause ionization to occur if it has the required energy. The energy to ionize a certain element is 530 kJ/mol. What wavelength contains enough energy in a single photon to ionize one atom of this element? Enter your answer with three significant figures.
(a) What is the frequency of radiation whose wavelength is 10.0 Å?
(b) What is the wavelength of radiation that has a frequency of 7.6 x 10 10 s-1?
(d) What distance does electromagnetic radiation travel in 25.5 fs?
How much total energy (in MJ/mol) would it take to remove the electrons from a mole of hydrogen atoms? The ionization energy for a hydrogen atom is 2.178 x 10-18 J. (A) 3.617 x 10 -42 MJ (B) 1.312 MJ (C) 2.765 MJ (D) 1.312 x 10 6 MJ (E) 2.765 x 10 35 MJ
What is the frequency of ultraviolet radiation having a wavelength or 46.3 nanometers? a) 1.54 x 10-14 s-1 b) 6.47 x 1015 s-1 c) 1.54 x 10-16 s-1 d) 6.47 x 1013 s-1 e) 1.18 x 10-7 s-1
An argon ion laser emits light at 532 nm. What is the frequency of this radiation? Using Figure 6.4, predict the color associated with this wavelength.
If the frequency of an X-ray is 5.4 x 10 18 Hz, what is the energy of one photon of this radiation? a) 3.6 x 10-15 J b) 1.6 x 10-27 J c) 1.2 x 10-52 J d) 2.7 x 10-10 J e) 7.4 x 10-29 J    
(a) A red laser pointer emits light with a wavelength of 650 nm. What is the frequency of this light?
A red laser pointer emits light with a wavelength of 650 nm. (b) What is the energy of one of these photons?
Calculate the energy of a photon of electromagnetic radiation at each of the following wavelengths. i) 632.8 nm (wavelength of red light from helium-neon laser)     ii) 503 nm (wavelength of maximum solar radiation)     iii) 0.0520 nm (a wavelength contained in medical X-rays)
Calculate the wavelength of each of the following frequencies of electromagnetic radiation.a. 101.9 MHZ (typical frequency for FM radio broadcasting)Delta1 =           m?b. 1020 KHZ (typical frequency for AM radio broadcasting) (assume four significant figures) Delta =            m?c. 835.6 MHZ (common frequency used for cell phone communication) Express your answer using four significant figures.Delta3 =         m?
If you put 120 volts of electricity through a pickle, the pickle will smoke and start glowing an orange-yellow color. The light is emitted because the sodium ions in the pickle become excited; their return to the ground state results in light emission (see Figure 6.13b and Sample Exercise 6.3). (a) The wavelength of this emitted light is 589 nrn. Calculate its frequency.
If you put 120 volts of electricity through a pickle, the pickle will smoke and start glowing an orange-yellow color. The light is emitted because the sodium ions in the pickle become excited; their return to the ground state results in light emission (see Figure 6.13b and Sample Exercise 6.3). (b) What is the energy of 0.10 mole of these photons?
An AM radio station broadcasts at 1010 kHz, and its FM partner broadcasts at 98.3 MHz. Calculate and compare the energy of the photons emitted by these two radio stations.
One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (a) What is the energy of a photon of this wavelength?
The wavelength of the green light is 530.0 nm. What is the frequency of green light?
One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (b) What is the energy of a mole of these photons?
One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (c) How many photons are in a 1.00 mJ burst of this radiation?
One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (d) These UV photons can break chemical bonds in your skin to cause sunburn—a form of radiation damage. If the 325-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.
The energy from radiation can be used to cause the rupture of chemical bonds. A minimum energy of 941 kJ/mol is required to break the nitrogen–nitrogen bond in N2. What is the longest wavelength of radiation that possesses the necessary energy to break the bond? What type of electromagnetic radiation is this?
A diode laser emits at a wavelength of 987 nm. (a) In what portion of the electromagnetic spectrum is this radiation found?
A stellar object is emitting radiation at 3.55 mm. (a) What type of electromagnetic spectrum is this radiation?
Sodium metal requires a photon with a minimum energy of 4.41 x 10 -19 J to emit electrons. (a) What is the minimum frequency of light necessary to emit electrons from sodium via the photoelectric effect?
Sodium metal requires a photon with a minimum energy of 4.41 x 10 -19 J to emit electrons. (b) What is the wavelength of this light?
Sodium metal requires a photon with a minimum energy of 4.41 x 10 -19 J to emit electrons. (d) What is the maximum number of electrons that can be freed by a burst of light whose total energy is 1 .00 μJ?
Use equation c=vλ and c=3.00 x 10 8 m/s to convert a wavelength of 3.5 x 10 -7 m to frequency (s-1).
The wavelength of some blue light is 470.0 nm. What is the frequency of this blue light?
Suppose that the microwave radiation has a wavelength of 12.4 cm. How many photons are required to heat 215 mL of coffee from 25.0 degree C to 62.0 degree C? Assume that the coffee has the same density, 0.997 g/mL, and specific heat capacity, 4.184 J/(g middot K), as water over this temperature range. Express the number of photons numerically.
A photon of light has a frequency of 3.26 x 1015 hertz. What is its wavelength? The speed of light is 2.998 x 108 m/s. a. 9.78 times 1014 nm b. 109 nm c. 1.09 times 107 nm d. 978 nm e. 92.0 nm
It takes 157 kJ/mol to break a nitrogen-oxygen single bond. Calculate the maximum wavelength of light for which a nitrogen-oxygen single bond could broken by absorbing a single photon.
The wavelength of some violet light is 420.0 nm. What is the frequency of this violet light?
The energy of light calculated using the formulas below tell you the energy per photon of light. E = h x v E = h x c / λ If light has a wavelength of 789 nm, what is the energy of this light expressed in kJ/mol? 
Microwave ovens emit microwave energy with a wavelength of 13.0 cm. What is the energy of exactly one photon of this microwave radiation? 
The frequency of the middle F note on a piano is 349.23 Hz. What is the wavelength of this note in centimeters? The speed of sound in air is 343.06 m/s.
Be sure to answer all parts. The blue color of the sky results from the scattering of sunlight by molecules in the air. The blue light has a frequency of about 7.09 x 1014 Hz. Calculate the wavelength (in nm) associated with this radiation, and calculate the energy (in joules) of a single photon associated with this frequency. Enter your answers in scientific notation (a) Wavelength of the radiation: (b) Energy (in joules) of a single photon: 
Be sure to answer all parts.What is the frequency (in reciprocal seconds) of electromagnetic radiation with a wavelength of 1.43 cm?Enter your answer in scientific notation.
For light with a wavelength of 8.20 μm, calculate the corresponding wave number value.  
Part A104.1 MHz (typical frequency for FM radio broadcasting) Express your answer in joules using four significant figures. Part B1045 MHz (typical frequency for FM radio broadcasting) Express your answer in joules using four significant figures. Part C839.7 MHz (typical frequency for FM radio broadcasting) Express your answer in joules using four significant figures.
Be sure to answer all parts.What is the wavelength (in nm) of radiation that has an energy content of 4.35 x 103 kJ/mol? 
The energy of a photon of light is given by E = hv. The frequency, v, of light and the wavelength, λ, are related through: v = c/λ where c is the speed of light, 2.998 x 108 m/s. Arrange the following wavelengths of light from lowest energy to highest energy by dragging them into the box below. What is the energy of a photon of light with a wavelength of 3.20 x 102 nm?
If the radio waves transmitted by a radio station have a frequency of 76.0 MHz, what is the wavelength of the waves, in meters?
Part AX-ray photons with a wavelength of 0.135 nm. Express the energy numerically in kilojoules per mole. Part Bγ-ray photons with a wavelength of 2.60 x 10-5 nm. Express the energy numerically in kilojoules per mole. 
What are the wavelengths, in nanometers, of the bright lines of the hydrogen emission corresponding to the transition: n = 5 to n = 2.
Be sure to answer all parts.The blue color of the sky results from the scattering of sunlight by molecules in the air. The blue light has a frequency of about 7.09 times 1014 Hz. Calculate the wavelength (in nm) associated with this radiation, and calculate the energy (in joules) of a single photon associated with this frequency. Enter your answers in scientific notation. (a) Wavelength of the radiation: (b) Energy (in joules) of a single photon:
The power of a red laser (λ = 630 nm) is 2.50 watts (abbreviated W, where 1 W = 1 J/s). How many photons per second does the laser emit?
How many photons are produced in a laser pulse of 0.580 J at 637 nm?
The wavelength of some red light is 700.5 nm. What is the frequency of this red light? 
How long does it take (in minutes) for light to reach Venus from the Sun, a distance of 1.117 times 10^6 km?
632.8 nm (wavelength of red light from a helium-neon laser) Express your answer using three significant figures.