Electron volts may sound like a strange unit,

one of many will come across in this course.

It is defined as the amount of energy that is gained or lost by the charge of a

single electron moving across an electric potential difference of 1 volt.

It is a minuscule amount of energy equivalent to about

1.6 times 10 to the minus 19 Joules.

The naming and labeling of light can be confusing.

The thing to remember is that a photon's energy, wavelength,

and frequency can all be considered as equivalent ways to describe light.

While a radio frequency photon emitted by a radio station is usually

characterized by its frequency, say 102.9 megahertz.

An X-ray photon is usually characterized by its energy,

say a kiloelectron volt.

Visible light photons are often described by their wavelength,

between 400 and 700 nanometers.

If you are given one of energy, frequency or wavelength,

there are some very simple mathematical relationships

that allow you to determine the other quantities.

The equation relating frequency and wavelength of a photon to the speed of light is,

the wavelength lambda times the frequency f is equal to

the speed of light c. Let's double check the values we had for our red laser.

We've been given its wavelength at 650 nanometers.

So to determine its frequency,

we simply divide the speed of light c by the wavelength lambda.

Remember, in order to calculate this properly,

we need to express both the speed of light and

the wavelength in the common unit of meters.

So, a red photon with a wavelength of

650 nanometers has an oscillation frequency of 460 terahertz,

exactly what I stated before.

How much energy is our 650 nanometer photon carrying?

Let's use our last answer of 460 terahertz to calculate the photon energy.

This time, we need another simple equation that

relates the frequency of a photon with the energy that it carries.

The photon energy is given by the equation,

E equals h times f. E

stands for the energy and f stands for the frequency of the photon.

But h is a new value in this equation.

This h represents Planck's constant,

named after Max Planck.

It relates the frequency of a photon with its energy.

H has a value of 6.626

times 10 to the minus 34 in units of Joule-seconds.

So, now our 650 nanometer wavelength photon

which oscillates with a frequency of 460 terahertz,

carries with it an energy equal to 3 times 10 to the minus 19 Joules.

That is a tiny amount of energy.

Each and every 650 nanometer wavelength photon

carries an incredibly small amount of energy.

But, bright light sources like lasers,

produce tremendous numbers of photons which is why

they pack enough punch to damage sensitive tissues like the retinas of our eyes.

Hence, the laser safety label,

that's common phrase in laser labs,

"Do not look into the laser with your remaining eye."

The relationships we have discussed here can be summed up in just three equations.

The first two we used,

that we just run through and a combination of them.

E is equal to hc over lambda.

These simple relationships are modern discoveries relatively speaking,

since they were developed in the early 20th century,

during the quantum revolution.

With these three equations,

a technological revolution occurred that permitted the development of advanced optics and

telescopes capable of measuring light from even the far reaches of the cosmos.

The speed of light is known to incredible precision.

Since the speed of light is well known,

it has become common for astronomers to measure enormous distances in space

in terms of the time it takes for light to travel in a given amount of time.

For example, the distance that light can travel in one second is known as a light-second.

One light-second is equal to 299,790,000

meters or 299,790 kilometers.

A number this large,

can be hard to wrap your head around.

So, let's compare this distance to one we can imagine.

The distance from the Earth and to the moon.

The distance between the Earth and the moon is 384,400 kilometers,

which is just a bit larger than one light-second.

We could use the unit kilometers which is getting a bit

crazy at this point or we could use the unit of light-second.

In this new unit,

the distance between the Earth and the moon is 1.3 light-seconds.

In other words, it takes a photon of light

1.3 seconds to travel from the Earth to the moon.

If we now step up the size scale and consider the Earth and our Sun,

it takes light 8.3 minutes to travel from the sun to the Earth.

So we say that the distance is 8.3 light-minutes.

Since the distance from the Earth to the sun is so important in astronomy,

astronomers also introduced a new distance

called the astronomical unit, abbreviated to AU.

An astronomical unit is the average distance between the Earth and the sun,

and is equal to 8.3 light-minutes

or 149.6 million kilometers.

Yeah, the measure of the distance in kilometers is starting to get a bit crazy and messy.

If we return to the speed of light measuring stick,

and continue to shift the size scale further,

we have had light-seconds and light-minutes minutes,

then a light-year is the distance light travels in one year.