Determine the energy of 1 mol of photons for each kind of light. (Assume three significant figur

Determine the energy of 1 mol of photons for each kind of...

Key Concepts

Planck's Equation

Planck's equation (E = hc/?) relates the energy of a photon to its wavelength. In this equation, h represents the Planck constant and c is the speed of light. This equation is fundamental in quantum mechanics and is used to determine the energy associated with a specific photon based on its wavelength.

Photon Energy

Photon energy is the discrete amount of energy carried by a single photon, and it is inversely proportional to its wavelength. Higher frequency (or shorter wavelength) photons have more energy, which is central to understanding processes such as photoelectric effect, spectroscopy, and various optical phenomena.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, defines the number of particles in one mole. When calculating the energy for a mole of photons, this constant is used to scale the energy of a single photon up to the macroscopic amount corresponding to one mole.

Unit Conversion

Unit conversion, particularly converting wavelengths from nanometers to meters, is key in applying Planck's equation correctly. Precise calculation requires converting all measurements to their SI units to ensure consistency and accuracy in the computed energy values.

Transcript

00:01 How's it going? for this question, we have to find the energy per mole, or energy for every one mole, in each of the infrared, visible light, and ultraviolet.

00:11 So the way we're going to do this problem here is we have to find some sort of expression for energy.

00:18 So, right here, i have energy equals to planx constant times new, which is the frequency.

00:25 But we do not have the frequency here, but we do have another relationship.

00:30 Between wavelength and frequency.

00:32 C equals to lambda times new, lambda being the wavelength and new being the frequency.

00:38 Here, we can rearrange the equation here to have new on one side, have c on the other side.

00:44 So we're going to have an expression, and we substitute the first new with the second new, and we're going to end up with energy equals to planx constant times c, speed of light in a vacuum, which is a constant, divided by lambda.

00:58 Here, we have the energy here, this is the energy per particle or photon when we're talking about light.

01:06 But here we have per one particle, but we have to find the energy per one mole.

01:12 So in this case, we have to introduce the avogalce number.

01:17 So this number, 6 .022 times 10 to the power of 23.

01:24 This is how many particles per mole? so if we have particles per mole, if we time the energy per particle here, with the avogadraous particle per mole here, we can see the units are going to cancel on, right? and we're going to leave one over mole, right? so in this case, we're going to get the energy per mole.

01:54 And this is on the grand scheme how we're going to do this question.

01:59 Right? so let's take a look.

02:00 For infrared, we're given a wavelength.

02:03 We can plug this number in.

02:05 We have e equals to plants constant, which we have 6 .63 times 10 to the power of negative 34, joules times a second.

02:20 After then, we have 3 times 10 to the power of 8 meters per second.

02:28 And finally, the wavelength, 1500 nanometers, and we're doing unit conversion because we want everything to be meters because we have a meters here.

02:39 So we're going to have for every one times 10 to the power of nine nanometers, we're going to have one whole meter.

02:46 So this is your unit conversion here.

02:49 And this is the energy per particle equation part here.

02:53 And now we want it to be per mole, right? so technically this should be, this equation should be expressed as one per particle.

03:05 Because we calculate, the energy per particle, right? but usually we don't include the per particle because we're not calculating energy per mole.

03:12 Right? and now we want to do the conversion.

03:15 We have 6 .022 times 10 to the power of 23 particle per per mole.

03:28 And now let's do a quick examination on the units.

03:31 We're going to have seconds cancel out.

03:34 Sorry for the messy writing, nanometers cancel out.

03:36 One meter cancel out with meters here...

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