**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 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?

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 10^{6} 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.

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

A popular kitchen appliance produces electromagnetic radiation with a frequency of 2450 MHz.
With reference to the figure below , answer the following:Estimate the wavelength of this radiation.

Electromagnetic waves. Like water waves, electromagnetic radiation can be characterized by a wavelength . Notice that the shorter the wavelength, l, the higher the frequency,
u. The wavelength in (b) is half as long as that in (a), and the frequency of the wave in (b) is therefore twice as great as the frequency in (a).If wave (a) has a wavelength of 4.0
m and a frequency of 3.0 108 cycles/s, what are the wavelength of wave (b)?

Define the wavelength and amplitude of a wave.

What is the wavelength of radiation that has a frequency of 5.60×1014 s-1 ?

Consider the two waves shown here , which we will consider to represent two electromagnetic radiations.What is the wavelength of wave A?

Consider the two waves shown here , which we will consider to represent two electromagnetic radiations.What is the wavelength of wave B?

A laser pointer used in a lecture hall emits light at 650 nm.What is the frequency of this radiation?

Moseley established the concept of atomic number by studying X-rays emitted by the elements. The X-rays emitted by some of the elements have the following wavelengths:
Element
Wavelength (Å)
Ne
14.610
Ca
3.358
Zn
1.435
Zr
0.786
Sn
0.491
Calculate the frequency,
Hz, of the X-rays emitted by each of the elements, in {
m Hz}.

How fast does it travel in a vacuum?

Define the frequency of electromagnetic radiation.

How is frequency related to wavelength?

What is the frequency of radiation that has a wavelength of 12 m , about the size of a bacterium?

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.The wavelength of this emitted light is 589 nm. Calculate its frequency.

Consider the two waves shown here , which we will consider to represent two electromagnetic radiations.What is the frequency of wave A?

Consider the two waves shown here , which we will consider to represent two electromagnetic radiations.What is the frequency of wave B?

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 frequency of light that has a wavelength of 340 nm .

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 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

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.

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

FM-95, an FM radio station, broadcasts at a frequency of 9.51 × 10 7 s−1 (95.1 MHz). What is the wavelength of these radio waves in meters?

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

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

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.

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)

(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?

Light travels at a speed of 2.998×108 m/s in a vacuum.What is the wavelength of radiation that has a frequency of 6.5×1011 s-1 ?

Light travels at a speed of 2.998×108 m/s in a vacuum.What distance does electromagnetic radiation travel in 0.44 ps ?

Calculate the wavelength of each of the following frequencies of electromagnetic radiation.102.6 MHz (typical frequency for FM radio broadcasting)

Calculate the wavelength of each of the following frequencies of electromagnetic radiation.1070 kHz (typical frequency for AM radio broadcasting)

Calculate the wavelength of each of the following frequencies of electromagnetic radiation.835.6 MHz (common frequency used for cell phone communication)

One reason carbon monoxide (CO) is toxic is that it binds to the blood protein hemoglobin more strongly than oxygen does. The bond between hemoglobin and CO absorbs radiation of 1953 cm−1. (The unit is the reciprocal of the wavelength in centimeters.) Calculate the wavelength (in nm and Å) and the frequency (in Hz) of the absorbed radiation.

An FM radio station found at 103.1 on the FM dial broadcasts at a frequency of 1.031 × 108 s−1 (103.1 MHz). What is the wavelength of these radio waves in meters?

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 wavelength of this radiation?

An FM radio station broadcasts at 99.5 MHz. Calculate the wavelength of the corresponding radio waves.

An AM station broadcasts rock music at “950 on your radio dial.” Units for AM frequencies are given in kilohertz (kHz). Find the wavelength of the station’s radio waves in meters (m), nanometers (nm), and angstroms (Å).

An FM station broadcasts music at 93.5 MHz (megahertz, or 10 6 Hz). Find the wavelength (in m, nm, and Å) of these waves.

The nearest star to our sun is Proxima Centauri, at a distance of 4.3 light-years from the Sun. A light-year is the distance that light travels in one year (365 days). How far away, in kilometers, is Proxima Centauri from the Sun?

Certain elements emit light of a specific wavelength when they are burned. Historically, chemists used such emission wavelengths to determine whether specific elements were present in a sample. Some characteristic wavelengths for some of the elements areAg328.1 nmFe372.0 nmAu267.6 nmK404.7 nmBa455.4 nmMg285.2 nmCa422.7 nmNa589.6 nmCu324.8 nmNi341.5 nmWhen burned, a sample of an unknown substance is found to emit light of frequency 9.23 x 1014 s–1. Which of these elements is probably in the sample?

Police often monitor traffic with “K-band” radar guns, which operate in the microwave region at 22.235 GHz (1 GHz = 109 Hz). Find the wavelength (in nm and Å) of this radiation.

Covalent bonds in a molecule absorb radiation in the IR region and vibrate at characteristic frequencies. The H—Cl bond has a frequency of vibration of 8.652 x 1013 Hz. What wavelength (in μm) corresponds to that frequency?

The speed of sound in air is 344 m/s at room temperature. The lowest frequency of a large organ pipe is 30 s-1 and the highest frequency of a piccolo is 1.5 x 104 s- 1. Find the difference in wavelength between these two sounds.

The distance from Earth to the sun is 1.5 x 108 km. Find the number of crests in a light wave of frequency 1.5×1014 s-1 traveling from the sun to the Earth.

Light travels at a speed of 2.998×108 m/s in a vacuum.What is the frequency of radiation whose wavelength is 0.82 nm ?

A green laser pointer emits light with a wavelength of 533 nm. What is the frequency of this light?

You may want to reference (Pages 214 - 216)Section 6.1 while completing this problem.Consider the following three statements:For any electromagnetic radiation, the product of the wavelength and the frequency is a constant.If a source of light has a wavelength of 3.0 Å, its frequency is 1.0 x 1018 Hz1.0 imes 10^{18}~
m Hz.The speed of ultraviolet light is greater than the speed of microwave radiation.Which of these three statements is or are true?

A laser dazzles the audience in a rock concert by emitting green light with a wavelength of 527 nm . Calculate the frequency of the light.

When rubidium ions is heated to a high temperature, a line is observed in its line spectrum at wavelength 7.9 × 10−7 m. What is the frequency of this line? What color do we see when we heat a rubidium compound?

When rubidium ions is heated to a high temperature, a line is observed in its line spectrum at wavelength 4.2 × 10−7 m. What is the frequency of this line? What color do we see when we heat a rubidium compound?

How much time (in seconds) does it take light in a vacuum to travel 1.00 billion km?

Calculate frequency of radiation that has a wavelength of 10 mm, about the size of a bacterium. Calculate the wavelength of radiation that has a frequency of 5.50 x 1014 s–1. Would the radiations be visible to the human eye?

Does the following equation describe particle-like or wavelike behavior? Does it involve both types of behavior?(a) c = λν

Mars is roughly 60 million km from the earth. How long does it take for a radio signal originating from the earth to reach Mars?

Determine which of the following statements are false, and correct them.(a) The frequency of radiation increases as the wavelength increases.(b) Electromagnetic radiation travels through a vacuum at a constant speed, regardless of wavelength.(c) Infrared light has higher frequencies than visible light.(d) The glow from a fireplace, the energy within a microwave oven, and a foghorn blast are all forms of electromagnetic radiation.

The laser in an audio CD player uses light with a wavelength of 7.80 x 10 2 nm. Calculate the frequency of this light.

Calculate the frequency of each of the following wavelengths of electromagnetic radiation.632.8 nm (wavelength of red light from a helium-neon laser)

Calculate the frequency of each of the following wavelengths of electromagnetic radiation.503 nm (wavelength of maximum solar radiation)

Calculate the frequency of each of the following wavelengths of electromagnetic radiation.0.0520 nm (a wavelength used in medical X rays)

A photon of light has a frequency of 3.26 x 10 15 hertz. What is its wavelength? The speed of light is 2.998 x 108 m/s. a. 9.78 x 1014 nm b. 109 nm c. 1.09 x 10 7 nm d. 978 nm e. 92.0 nm

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)

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 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?

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.

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:

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 (s -1) 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?

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?

Human color vision is “produced” by the nervous system based on how three different cone receptors interact with photons of light in the eye. These three different types of cones interact with photons of different frequency light, as indicated in the following chart:What wavelength ranges (and corresponding colors) do the three types of cones detect?

Photosynthesis uses 660-nm light to convert CO 2 and H2O into glucose and O 2. Calculate the frequency of this light.

The laser on a Blu-ray player has a wavelength of 405 nm. In what region of the electromagnetic spectrum is this radiation? What is its frequency?

The distance from the sun to Earth is 1.496×108 km. How long does it take light to travel from the sun to Earth?

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)

Octyl methoxycinnamate and oxybenzone are common ingredients in sunscreen applications. These compounds work by absorbing ultraviolet (UV) B light (wavelength 280–320 nm), the UV light most associated with sunburn symptoms. What frequency range of light do these compounds absorb?

632.8 nm (wavelength of red light from a helium-neon laser) Express your answer using three significant figures. v1 = s -1

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)

How many photons are produced in a laser pulse of 0.528 J at 679 nm?

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.