### Wavelength and Frequency Calculations - Chemistry LibreTexts

A2A [math]\implies K.E = \dfrac{p^2}{2m}[/math] [math]\implies \boxed{p = \sqrt{ 2m(K.E)}}[/math] where, [math]K.E[/math] = Kinetic Energy [math]m[/math] = Mass . c = × m/s. 1 m = 1 × nm. 1 kJ = J example. Light with a wavelength of nm is green. Calculate the energy in joules for a green light photon. The greater the energy, the larger the frequency and the shorter (smaller) the wavelength. Given the relationship between wavelength and frequency — the.

We could measure a velocity for the wave if we measure how far horizontally a crest travels in a unit of time. We also need to determine a very important characteristic of waves called frequency. If we choose an exact position along the path of the wave and count how many crests pass the position per unit time, we would get a value for frequency. The proper unit for frequency has seconds in the denominator and "1" in the numerator. This unit has been named "Hertz".

Unfortunately, this Greek letter looks a very great deal like an italicized v. To avoid this problem, this material will use a lower case f as the symbol for frequency.

Electromagnetic Waves[ edit ] Electromagnetic radiation light waves are somewhat like waves in a rope … except without the rope. Light waves do not need a medium through which to travel. They can travel through a vacuum, which is obvious since they come to us from the sun. The energy of an electromagnetic wave travels in a straight line along the path of the wave just as did the energy in a rope wave.

The moving light has associated with it an oscillating electric field and an oscillating magnetic field. This means that along the straight line path of the wave, there exists a positive electric field that will reach maximum positive charge, then slowly collapse to zero charge, and then expand to a maximum negative charge.

Along the path of the electromagnetic wave, this changing electric field repeats its oscillating charge over and over again. There is also a changing magnetic field that oscillates from maximum north pole field to maximum south pole field.

When scientists try to draw a picture to represent this concept, they use the same picture of a wave that was used for rope waves and water waves. You should not allow yourself to think that the light travels in this waving pattern. The light travels along the straight red line that represents the undisturbed position.

For an electromagnetic wave, the crests and troughs represent oscillating fields, not the path of the light.

### Wavelength, Frequency, Amplitude, & Intensity - CHEMISTRY COMMUNITY

We can still characterize light waves by their wavelength, frequency, and velocity but these values will be significantly different numerically from water and rope waves. At some point along the path of the electromagnetic wave, the electric field will reach a maximum value crest and then, as the electromagnetic wave continues to move along its straight line path, the electric field will decrease, through zero, increase to a maximum trough, collapse back to zero again, and then expand to another maximum crest.

We can measure along the path of the wave, the distance the wave travels between one crest and the succeeding crest and this distance will be the wavelength of the wave. The frequency of electromagnetic waves are determined in the same way as the frequency of a rope wave, that is, the number of full cycles that pass a point in a unit of time.

### What is the relationship between wavelength, frequency, and energy of a photon? | Socratic

The velocity of electromagnetic waves in a vacuum is the same for all waves regardless of frequency or wavelength. Every electromagnetic wave has a velocity of 3. The velocity of electromagnetic waves in air is slightly less than in a vacuum but so close that we will use the value for the velocity.

The speed of light in a vacuum is symbolized by a lower case c. In rope waves and water waves, the amount of energy possessed by the wave is related to the amplitude of the wave; more energy is put into the rope if the end of the rope is jerked higher and lower. But, in electromagnetic radiation, the amount of energy possessed by the wave is related only to the frequency of the wave.

In fact, the frequency of an electromagnetic wave can be converted directly to energy in joules by multiplying by a conversion factor.

The conversion factor is called Planck's constant and is equal to 6. The Electromagnetic Spectrum[ edit ] Electromagnetic waves have an extremely wide range of wavelengths, frequencies, and energies.

On the far left of Figure 5. These are called gamma rays and can be quite dangerous, in large numbers, to living systems. The next lower energy form of electromagnetic waves are called x-rays.

Most of you are familiar with the penetration abilities of these waves. They can also be dangerous to living systems. Humans are advised to limit as much as possible the number of medical x-rays they have per year.

Next lower, in energy, are ultraviolet rays. These rays are part of sunlight and the upper end of the ultraviolet range can cause sunburn and perhaps skin cancer.

The tiny section next in the spectrum is the visible range of light … this section has been greatly expanded in the bottom half of the figure so it can be discussed in more detail. The visible range of electromagnetic radiation are the frequencies to which the human eye responds. Lower in the spectrum are infrared rays and radio waves. The light energies that are in the visible range are electromagnetic waves that cause the human eye to respond when those frequencies enter the eye.

The eye sends a signal to the brain and the individual "sees" various colors. The highest energy waves in the visible region cause the brain to see violet and as the energy decreases, the colors change to blue, green, yellow, orange, and red.

When the energy of the wave is above or below the visible range, the eye does not respond to them. When the eye receives several different frequencies at the same time, the colors are blended by the brain. If all frequencies of light strike the eye together, the brain sees white and if there are no visible frequencies striking the eye, the brain sees black.

The objects that you see around you are light absorbers - that is, the chemicals on the surface of the object will absorb certain frequencies and not others. Your eyes detect the frequencies that strike your eye. You'd see these four lines of color. So, since you see lines, we call this a line spectrum. So this is the line spectrum for hydrogen. So you see one red line and it turns out that that red line has a wave length.

## CHEMISTRY COMMUNITY

That red light has a wave length of nanometers. You'll also see a blue green line and so this has a wave length of nanometers. A blue line, nanometers, and a violet line at nanometers. And so this emission spectrum is unique to hydrogen and so this is one way to identify elements. And so this is a pretty important thing. And since line spectrum are unique, this is pretty important to explain where those wavelengths come from.

And we can do that by using the equation we derived in the previous video. So I call this equation the Balmer Rydberg equation. And you can see that one over lamda, lamda is the wavelength of light that's emitted, is equal to R, which is the Rydberg constant, times one over I squared, where I is talking about the lower energy level, minus one over J squared, where J is referring to the higher energy level.

For example, let's say we were considering an excited electron that's falling from a higher energy level n is equal to three. So let me write this here.

So we have an electron that's falling from n is equal to three down to a lower energy level, n is equal to two. All right, so it's going to emit light when it undergoes that transition. So let's look at a visual representation of this.

Now let's see if we can calculate the wavelength of light that's emitted. All right, so if an electron is falling from n is equal to three to n is equal to two, I'm gonna go ahead and draw an electron here.

## 5.2: Wavelength and Frequency Calculations

So an electron is falling from n is equal to three energy level down to n is equal to two, and the difference in those two energy levels are that difference in energy is equal to the energy of the photon. And so that's how we calculated the Balmer Rydberg equation in the previous video. All right, let's go ahead and calculate the wavelength of light that's emitted when the electron falls from the third energy level to the second.

So, we have one over lamda is equal to the Rydberg constant, as we saw in the previous video, is one point zero nine seven times ten to the seventh. The units would be one over meter, all right? One over I squared. So, I refers to the lower energy level, all right? So the lower energy level is when n is equal to two. So we plug in one over two squared. And then, from that, we're going to subtract one over the higher energy level. That's n is equal to three, right? So this would be one over three squared.

So one over two squared minus one over three squared. Let's go ahead and get out the calculator and let's do that math.

So one over two squared, that's one fourth, so that's point two five, minus one over three squared, so that's one over nine. So, one fourth minus one ninth gives us point one three eight repeating. And if we multiply that number by the Rydberg constant, right, that's one point zero nine seven times ten to the seventh, we get one five two three six one one. So let me go ahead and write that down. So now we have one over lamda is equal to one five two three six one one.

So to solve for lamda, all we need to do is take one over that number. So one over that number gives us six point five six times ten to the negative seven and that would now be in meters. So we have lamda is equal to six point five six times ten to the negative seventh meters. So let's convert that into, let's go like this, let's gothat's the same thing as times ten to the negative ninth meters.

And so that's nanometers. All right, so let's go back up here and see where we've seen nanometers before.

So, that red line represents the light that's emitted when an electron falls from the third energy level down to the second energy level. So let's go back down to here and let's go ahead and show that.

So we can say that a photon, right, a photon of red light is given off as the electron falls from the third energy level to the second energy level. So that explains the red line in the line spectrum of hydrogen.

So how can we explain these other lines that we see, right? So we have these other lines over here, right?