Electromagnetic Spectrum, Frequency & Wavelength

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: The Electromagnetic Spectrum

Video Transcript

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

Video Transcript

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

Video Transcript

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 proportionally, meaning that if one increases then the other one must be decrease. 

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


Wavelength & Frequency Calculations

Concept: Converting between Wavelength & Frequency

Video Transcript

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 106 Hertz) find the wavelength in μm and Å of the radio waves.  


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


Electromagnetic Spectrum, Frequency & Wavelength Additional Practice Problems

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

Watch Solution

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

Watch Solution

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

Watch Solution

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

Watch Solution

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


Watch Solution

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


Watch Solution

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


Watch Solution

Determine the longest wavelength of light required to remove an electron from a sample of potassium metal, if the binding energy for an electron in K is 1.76 × 103 kJ/mol.

A) 113 nm

B) 885 nm

C) 68.0 nm

D) 147 nm

E) 387 nm


Watch Solution

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


Watch Solution

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


Watch Solution

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

Watch Solution

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


Watch Solution

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

Watch Solution

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?

Watch Solution

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°?

Watch Solution

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

Watch Solution

Which of the responses contains all the true statements and no others regarding electromagnetic radiation (light)?

I. As energy increases frequency decreases.

II. As wavelength increases energy decreases.

III. As wavelength increases frequency decreases.

IV. The product of wavelength and frequency is constant.

a) I, III and IV

b) I and II

c) I, II and IV

d) II, III and IV

e) III and IV

Watch Solution

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 an 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 1012-1




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. 

Watch Solution

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

Watch Solution

What wavelength of light will be required to remove an electron from the n = 3 shell of a hydrogen atom?

Watch Solution

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

Watch Solution

Assuming an ionization efficiency of 18.0%, how many photons are needed to ionize 1.00 x 1016 atoms?

Watch Solution

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

Watch Solution

R = 2.18x10-18 J;  h = 6.626x10-34 J•sec or 6.626x10-34 kg•m2 sec-1;  

c = 3.00 x 10 8 m•sec-1; 1eV= 1.602x10-19 J


a.) What is the energy of a photon with a wavelength of 335 nm?





b.) If a metal that has a work function of 2.80 eV, what wavelength of light is required to generate electrons with a kinetic energy of 1.02 eV?







c.) If a reaction is exothermic, does it mean that ΔE for the reaction is negative? Explain.




Watch Solution

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

Watch Solution

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









Watch Solution

Determine the shortest frequency of light required to remove an electron from a sample of a metal, if the binding (threshold) energy of the metal is 3.14x103 kJ/mol.


a. 7.87x1015 Hz

b. 4.74x1015 Hz

c. 2.11x1015 Hz

d. 1.27x1015 Hz

e. 6.19x1015 Hz 

Watch Solution

Determine the longest wavelength of light required to remove an electron from an atom of a metal, if the binding energy for an electron in that metal is 309 kJ/mol.

a. 147 nm

b. 68.0 nm

c. 113 nm

d. 885 nm

e. 387nm

Watch Solution

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

Watch Solution

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

Watch Solution

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

Watch Solution

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

Watch Solution

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

Watch Solution

Which of the following statements is NOT true?


a) Energy increases as the wavelength decreases.

b) Energy increases as the frequency increases.

c) Frequency increases as the wavelength decreases.

d) All of the statements are true.

Watch Solution

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

Watch Solution

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

Watch Solution

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

Watch Solution

As the wavelength of light increases, which is also true of light?

A. frequency decreases and energy decreases

B. frequency decreases and energy increases

C. frequency increases and energy decreases

D. frequency increases and energy decreases

E. frequency and energy remain constant

Watch Solution

Which wave form for a particle trapped in a 1-dimensional box has the highest energy?



Watch Solution

Which wave form for a particle trapped in a 1-dimensional box has the lowest energy?


Watch Solution