The Energy of Light: Videos & Practice Problems

Light is composed of particles known as photons, a concept introduced by physicists Max Planck and Albert Einstein. The energy of a photon can be calculated using Planck's constant (h), which is 6.626 x 10^-34 joules seconds. There are two key formulas for determining the energy of a photon: one involving its frequency:

$E=hf$

where frequency is measured in hertz, and the other its wavelength:

$E=\frac{hc}{\lambda }$

with wavelength measured in meters. Energy is directly proportional to frequency and inversely proportional to wavelength. To find the energy of a mole of photons, Avogadro's number (6.022 x 10²³ photons/mole) is used as a conversion factor, allowing the transition from energy per photon to energy per mole of photons. This relationship is crucial for understanding the behavior of light and its quantized nature in the realm of quantum mechanics.

Photons and Planck's Constant

He were going to say that the physicist Max Planck and Albert Einstein theorized that light was made of packets of or particles of electromagnetic radiation. Now we're going to say that this light particle or packet are referred to as a photon, and if we're talking about a cluster of them, we can also use the term quantum.

Now to calculate its energy, we use Planck's constant when it comes to light and it uses the variable H and it's equal to 6.626 × 10 -34 J×s. So just keep in mind when we're looking for the energy of light we're going to incorporate planks constant O.

Now that we know this, click onto the next video and let's take a look at some formulas that are important when calculating the energy of light.

Photon Energy Formulas

So when it comes to calculating the energy of light in the form of a photon, we have two different formulas that we can rely on and realize. Only one of them has a purple box around it. So that one is the more commonly used formula, and that's the one you should keep in mind and memorize. So we're going to say here the first version is used when we deal with energy and frequency. So here it's going to say that change in energy or energy of a photon in joules per photon equals Planck's constant which is H times frequency which is in seconds, inverse or Hertz. So remember frequency uses the on Greek symbol MU.

Now the other one we use when we're dealing with calculating the energy of a photon when given energy and wavelength in this one we're going to say change in energy or energy of a photon in joules over photons equals Planck's constant still, but now it's times the speed of light divided by wavelength in meters. So just remember two different formulas, one we use when we're dealing with frequency and energy and the other one we use when we're dealing with wavelength and energy.

Now from the equations realize that this tells us that energy is directly proportional to frequency. Meaning that if your energy is going up, your frequency is going up and it would be inversely proportional, inversely proportional to wavelength. That means that if your energy or frequency are increasing, that means wavelength would have to be would have to be decreasing. So just keep in mind the relationships that we have between now energy, frequency and wavelength.

E = h ⁢ ν E = h ⁢ c λ

Photon Energy Example

Here we're told to calculate the energy of a photon with a wavelength of 293.7 meters. Here they're giving us wavelength of the photon and they're asking for energy. So we're going to use the second formula where the energy of a photon equals Planck's constant time, the speed of light divided by our wavelength.

Here Planck's constant is 6.626×10-34 joules times seconds. Speed of light is 3.00×108 meters per second and then we have our wavelength which is 293.7 meters. Here, seconds cancel out with seconds. Meters cancel out with meters. That leaves us joules as our remaining unit.

But remember, this is joules per photon. Here this comes out to 6.768×10-28 joules per photon. Here our value has four sig figs because our 293.7 meters given to us initially also has four significant figures.

Moles and Photon Energy

Now up to this point, we know how to calculate the energy of 1 photon, and we know the units here would be joules per photon. Now in order to find the energy for a mole of photons, we can use the conversion factor with Avogadro's number.

Now, here, the conversion factor would be 1 mole of photons equals 6.022×1023 photons. So we know that that value represents Avogadro's number. So just remember, when we calculate the joules per photon from our formulas, we can use Avogadro's number to convert it into joules per mole of photons.

Now we know this connection, move on to the next video and let's put it to work.

Moles and Photon Energy Example

Here it says to calculate the energy for molophotons with the frequency of 4.29 * 10¹⁵ seconds^-1. All right, So what we're going to have here is we have energy and they're giving us frequency. So we're going to say here, energy of a photon equals Planck's constant times frequency. So that's going to be 6.626 * 10^-34 Joules times seconds. That's Planck's constant times our frequency in seconds^-1.

So here seconds will cancel out with inverse seconds, and when we get initially is 2.842554 * 10^-18 joules per photon. Remember, we don't want to round until the very end. So now that we have joules per photon realized, we need to find it in terms of moles of photons O we're going to use our conversion factor O. We're going to say here that we have for everyone mole of photons, we have 6.022 * 10²³ photons.

So here photons cancel out. And I'll have my answer in joules per mole of photons. So this comes out to 1.71 * 10⁶ joules per mole of photons. OK, so now our answer here is 366 because our initial value also had three sig figs.

Calculate the energy (in nJ) of a photon emitted by a mercury lamp with a frequency of 6.88 x 10¹⁴ Hz.

• A. 5.46 x 10^-9 nJ
• B. 9.89 x 10^-9 nJ
• C. 2.89 x 10^-10 nJ
• D. 4.56 x 10^-10 nJ

Answer: (D)

A light ray has a wavelength that is 835 µm contains 6.32 x 10^-3 J of energy. How many photons does this light ray have?

• A. 7.98 x 10¹⁸ photons
• B. 4.85 x 10¹⁹ photons
• C. 9.48 x 10¹⁸ photons
• D. 2.65 x 10¹⁹ photons

Answer: (D)

How much energy (in kJ) do 4.50 moles of photons contain at a wavelength of 705 nm?

• A. 2.58 x 10² kJ
• B. 7.64 x 10² kJ
• C. 8.45 x 10² kJ
• D. 5.89 x 10² kJ

Answer: (B)

Here’s what students ask on this topic:

What is a photon?

A photon is a fundamental particle that represents the quantum of light or other electromagnetic radiation. It is the carrier of the electromagnetic force, even when static via virtual photons. Photons are unique because they have no mass and always move at the speed of light in a vacuum, which is approximately 299,792 kilometers per second (or about 186,282 miles per second).

Photons exhibit both wave-like and particle-like properties, a duality that is a cornerstone of quantum mechanics. When considering light as a wave, it is characterized by its wavelength or frequency. However, when considered as particles, interactions of light with matter, such as absorption and emission, are best described as discrete packets of energy, or quanta, which we call photons.

The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength. This relationship is expressed by the equation:

$E=hf$

where E is energy, h is Planck's constant, and f is the frequency of the photon. This quantized nature of light plays a critical role in understanding phenomena such as the photoelectric effect, lasers, and the behavior of atoms and molecules.

What is Planck's constant?

Planck's constant is a fundamental physical constant denoted by the symbol 'h' that relates the energy of a photon to the frequency of its electromagnetic wave. It is a key quantity in quantum mechanics, a branch of physics that deals with the behavior of particles at the atomic and subatomic levels.

The constant is named after Max Planck, the physicist who proposed it in 1900. Planck discovered that energy is not exchanged continuously but rather in discrete amounts called quanta. The value of Planck's constant is approximately 6.62607015 x 10^-34 joule-seconds. This small number indicates that the energy quanta are very tiny, which is why quantum effects are not noticeable in everyday life.

The equation $E=hf$ illustrates the direct proportionality between the energy (E) of a photon and its frequency (f), with Planck's constant (h) being the proportionality factor. This relationship is pivotal for understanding phenomena such as the photoelectric effect, and it laid the groundwork for the development of quantum theory.

What does Planck's constant represent?

Planck's constant is a fundamental physical constant denoted by the symbol 'h' that is crucial in the field of quantum mechanics. It represents the proportionality constant that relates the energy of a photon (the smallest quantum of light) to its frequency. The exact value of Planck's constant is approximately 6.62607015 x 10^-34 joule seconds. This constant is named after the physicist Max Planck, who first proposed it in 1900.

In the equation $E=hf$, 'E' stands for energy, 'h' is Planck's constant, and 'f' is the frequency of the photon. The introduction of Planck's constant marked a significant departure from classical physics, indicating that energy, at a microscopic level, is quantized and can only exist in discrete amounts rather than a continuous range. This quantization is the cornerstone of quantum theory, which governs the behavior of particles at atomic and subatomic scales.