**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:** The Electromagnetic Spectrum

Welcome back guys. In this new video, we're going to take a look at the nature of light. Now, what we should realize is the visible light that we see with our eyes, it only represents a small section of all the possible lights that exists. The visible light that we see has a certain energy tied with it.

Now, there are light sources that are above that energy and below that energy. Taking into account all of these different types of energies, we have this image right here. This is known as our electromagnetic spectrum. You should see that we have here, these are gamma rays, we have X-rays, UV, here this is infrared, IR.

Now, between UV which is ultraviolet light and IR, which is infrared light, that's what we find our visible light spectrum. We're going to say our visible light spectrum—the range is really 390 nm to about 780 nm. We learned this in the school, roygbiv, so roygbiv. Remember, what is that stand for? We're going to say red, orange, yellow, green, blue, indigo and violet.

We're going to say here, it looks like violet, violet is around 400 nm, whereas red is around 780 nm. Remember, the visible light spectrum only represent a small section of the entire spectrum of colors. Now, after IR, there are these microwave, then we have radio waves, which we get in our car radios or at home, on our stereos. We have FM and then we have radio in between AM and then we have long radio waves.

These represent basically all the different types of light sources or light energies that exist. There is also a cosmic rays which are usually above gamma, the professors usually ignore those.

**Concept:** Wavelength & Frequency

We're going to say according to this graph, there are basically wave properties associated with this electromagnetic spectrum.

We're going to say there are two independent variables associated with this electromagnetic spectrum. We're going to say the first one uses the variable V which really stands for mu, the Greek mu. In it is the number of waves you have per second, that right there would be our frequency. It is expressed in units of seconds inverse or hertz. Just remember, seconds inverse or hertz mean the same exact thing.

The second variable associated with our electromagnetic spectrum is lambda. This represents the distance from one quest of a wave to the other and this is our wavelength. The units for wavelength are meters. We're going to say that in our electromagnetic spectrum, we have frequency and we have wavelength.

**Concept:** The relationship between Wavelength & Frequency

As you can see, we're going to say, it looks like long radio waves, they have the highest wavelength, because they're above 108 meters, but as a result their frequency is very low, so they would have the lowest frequency. On the other side, it looks like gamma rays is 10/24 for frequency, so these guys would have the highest frequency and on the bottom, therefore it'd have the lowest wavelength.

Looking out what happens to our frequency when our wavelength is affected. Remember, we've talked about this before, we would say that the relationship between frequency and wavelength is that they are inversely proportional, which means they're opposite of one another. The way you should understand it visually is like this, so we have light travels sometimes as waves according to some theories. Here are some waves. These represent a bunch of light particles together.

Now, what we're going to say here is that frequency is how many waves do you get per second? Then, here we're going to say that wavelength is the distance from one top of the wave to the other. In this image here, we'd say that, the distance is pretty big, so we'd say that the wavelength is high, but we only get three waves in a second. That's not that many. We'd say that our frequency is low.

Now, if we draw a different picture, this is roughly the same distance as the first set of waves that I've showed you, but here now, you would say that the distance from one top of the wave to the other decrease. The wavelength looks like it's very small, so the wavelength would be low. We also say that we get a lot more waves per second, for that period of time, so we'd say that frequency here is high.

Visually, this is how you would show that frequency and wavelength are inversely proportional. Meaning that they are opposite of one another. We've talked about this when we talked about the relationship between certain factors such as pressure and volume. They're inversely proportional to each other. Same way, wavelength and frequency are inversely proportional.

Now, what this have to do with our electromagnetic spectrum? Our electromagnetic spectrum is a way of associating light with energy. We're going to say here, highest frequency, frequency has a direct relationship to energy. We'd say that gamma rays according to this spectrum have the highest frequency and therefore they have the highest energy. So they're both directly related to each other.

Remember, wavelength and frequency are opposites of one another. If my energy is high, therefore my wavelength would be low. On this other side, because my frequency is low, that means my energy is low.

It's going to become important that you guys remember the order of these different types of light sources, because your professor will easily ask one of them on the exam, 'Rank these in terms of increasing energy. Rank these in terms of increasing frequency.' It becomes important to remember the order.

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

**Problem:** 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:** Converting between Wavelength and Frequency

In this new video, we're going to continue our discussions of the relationship between frequency and wavelength and see how do we mathematically go from one to the other. We're going to say that the speed of a wave or speed of a light wave is the product of the frequency times the wavelength or between mu

times lambda. We're going to say in a vacuum, all forms of radiation travel at a constant 3.00 times 10 to the 8 meters per second. This is a physical constant that's known as the speed of light. We're going to say the speed of light just equals our wavelength times our frequency.

Basically, we're going to look at this equation right here. With this his equation, we’re able to go from frequency to wavelength because C is always that number, 3.00 times 10 to the 8 meters per second.

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

**Example:** 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.

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

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.

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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 10^{14} 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:

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For light with a wavelength of 8.20 μm, calculate the corresponding wave number value.

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The wavelength of some red light is 700.5 nm. What is the frequency of this red light?

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How long does it take (in minutes) for light to reach Venus from the Sun, a distance of 1.117 times 10^6 km?

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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 10^{8} m/s.

a. 9.78 times 10^{14} nm

b. 109 nm

c. 1.09 times 10^{7} nm

d. 978 nm

e. 92.0 nm

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Some copper compounds emit green light when they are heated in a flame. How would you determine whether the light is of one wavelength or a mixture of two or more wavelengths?

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What are the units for wavelength and frequency of electromagnetic waves? What is the speed of light in meters per second and miles per hour?

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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) of this radiation.

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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.

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The wavelength of some blue light is 470.0 nm. What is the frequency of this blue light?

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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)

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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)

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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)

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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?

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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}).

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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.

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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.

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

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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)

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How many photons are contained in a flash of green light (525 nm) that contains 189 kJ of energy?

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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)

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How many photons are contained in a flash of green light (525 nm) that contains 189 kJ of energy?

(a) 4.99 x 10^{23}

(b) 7.99 x 10^{30}

(c) 5.67 x 10^{23}

(d) 1.25 x 10^{31}

(e) 3.75 x 10^{23}

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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)

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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.

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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

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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?

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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 10^{8} 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?

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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 10^{6} nm

**D) **5.51 x 10^{14} nm

**E) **654 nm

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A laser pulse produces 1.046 kJ of energy. It was experimentally determined that the pulse contains 3.50 x 10^{22} photons. Determine the wavelength of light (in meters) emitted by one photon.

**A) **6.65 x 10^{-3} m

**B) **1.50 x 10^{5} m

**C) **5.43 x 10^{-48} m

**D) **1.50 x 10^{2} m

**E) **6.65 x 10^{-6} m

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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 10^{4}

e) 2.5

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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}

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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^{-7}s^{-1}

b) 5.96 x 10^{11 }s^{-1}

c) 3.59 x 10^{35} s^{-1}

d) 3.59 x 10^{38 }s^{-1}

e) 5.96 x 10^{14 }s^{-1}

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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 10^{2 }

B. 1.60 x 10^{2}

C. 480 x 10^{2 }

D. 480 x 10^{3}

E. 5.30 x 10^{3}

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Calculate the frequency of visible light having a wavelength of 686 nm.

A) 4.37 x 10^{14} /s

B) 4.37 x 10^{5} /s

C) 2.06 x 10^{2} /s

D) 2.29 x 10^{-15} /s

E) 2.29 x 10^{-6 }/s

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An ultraviolet (UV) light photon has a wavelength of 124.1 nm. What is its energy in joules?

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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

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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

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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

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A line in the spectrum of an element was observed to have a frequesncy of 5.17 x 10^{14} s ^{-1} . What is the wavelength of this radiation?

a. 5.80 x 10^{-7} meters

b. 1.72 x 10^{6} meters

c. 1.55 x 10^{23} meters

d. 1.77 x 10^{-4} meters

e. 174 meters

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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 10^{14} s^{-1}

B) 4.1 x 10^{14} s^{-1}

C) 8.2 x 10^{14} s^{-1}

D) 8.2 x 10^{15} s^{-1}

E) 4.1 x 10^{15} s^{-1}

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What is the frequency of the medical X-ray at 0.052 nm?

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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 10^{13} Hz

B) 6.0 x 10^{13} Hz

C) 1.7 x 10^{-14 }Hz

D) 2.0 x 10^{5} 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

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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

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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.

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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 10^{20} atoms

2. 7.11 x 10^{24} atoms

3. 1.50 x 10^{19} atoms

4. 1.08 x 1017 atoms

5. 7.86 x 10^{−19} atoms

6. 4.73 x 10^{5} atoms

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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.

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The energy of a photon is

1. nλ.

2. cλ.

3. c/λ .

4. λ/hc .

5. hc/λ .

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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

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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 × 10^{5} J

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How many photons of light with frequency 5.50 × 10 ^{15} Hz are required to provide 1 kJ of energy?

A) 2.74 × 10^{20} photons

B) 3.64 × 10^{-16} photons

C) 3.64 × 10^{-18} photons

D) 4.56 × 10^{-4} photons

E) 1.65 × 10^{44} photons

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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 × 10^{3} kJ/mol

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Use Planck's equation to determine the energy, in J/photon, of radiation of frequency 5.8 × 10^{15} 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 ×10^{24} J

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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 ×10^{11}

B) 5.71 ×10^{5}

C) 1.75 ×10^{-15}

D) 5.71 ×10^{14}

E) 1.58 ×10^{2}

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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

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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

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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 × 10^{30} photons

B) 2.48 × 10^{25} photons

C) 1.81 × 10^{24} photons

D) 3.37 × 10^{19} photons

E) 4.03 × 10^{28} photons

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Calculate the energy of the orange light emitted by a neon sign with a frequency of 4.89 × 10^{14} 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

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Calculate the frequency of the green light emitted by a hydrogen atom with a wavelength of 486.1 nm.

A) 6.17 ×10^{14} s^{-1}

B) 1.46 ×10^{14} s^{-1}

C) 4.33 ×10^{14} s^{-1}

D) 1.62 ×10^{14} s^{-1}

E) 6.86 ×10^{14} s^{-1}

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Calculate the frequency of the red light emitted by a neon sign with a wavelength of 659.9 nm.

A) 4.55 ×10^{14} s^{-1}

B) 1.98 ×10^{14} s^{-1}

C) 3.32 ×10^{14} s^{-1}

D) 5.05 ×10^{14} s^{-1}

E) 2.20 ×10^{14} s^{-1}

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Calculate the wavelength (in nm) of the blue light emitted by a mercury lamp with a frequency of 6.88 ×10^{14} Hz.

A) 229 nm

B) 206 nm

C) 436 nm

D) 675 nm

E) 485 nm

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Calculate the wavelength (in nm) of the red light emitted by a neon sign with a frequency of 4.74 ×10^{14} Hz.

A) 704 nm

B) 158 nm

C) 466 nm

D) 142 nm

E) 633 nm

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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 × 10^{5} J

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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 ×10^{18}

C) 1.04 × 10^{-22}

D) 1.04 × 10^{-31}

E) 3.79 ×10^{-19}

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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} J

b. 3.08 x 10^{-31} J

c. 1.4 x 10^{-27} J

d. 4.27 x 10^{-19} J

e. 1.79 x 10^{-18} J

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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

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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

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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?

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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

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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°?

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How much energy is contained in 2.5 moles of 455 nm photons?

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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

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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 10^{15} s^{-1}

c) 1.54 x 10^{-16} s^{-1}

d) 6.47 x 10^{13} s^{-1}

e) 1.18 x 10^{-7} s^{-1}

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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

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What is the wavelength of yellow light (in nanometers) having a frequency of 5.17 x 10^{14} 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 10^{2} m

e) 1.72 x 10^{4} m

Watch Solution

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.

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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 10^{12} Hz = 1 x 10^{12} 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.

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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

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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

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The carcinogen, CCl_{4 }has been dumped into a holding pond. CCl_{4} will begin to decompose by the following reaction:

CCl_{4} → Cl_{3}C• + 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 10^{14 } Hz. Can you expect sunlight alone to affect the decomposition?

Explain. h= 6.63 x 10 ^{-34} J•sec; c = 3.00 x 10^{8} m/sec

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The carcinogen, CCl_{4 }has been dumped into a holding pond. CCl_{4 }will begin to decompose by the following reaction:

CCl_{4} → Cl_{3}C• + 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

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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

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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

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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 }photons

B. 2.74 x 10 ^{20} photons

C. 3.64 x 10 ^{-16} photons

D. 3.64 x 10 ^{-18} photons

E. 4.56 x 10 ^{-4} photons

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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}

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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

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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}

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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

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Determine the wavelength (in nm) of an X-ray with a frequency of 4.2 × 10 ^{18}Hz.

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}

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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

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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

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