¿Cuál es la longitud de onda (en metros) de los fotones con las siguientes energias? ¿En qué reg

step 1 Okay, to solve this, we are going to start with our equation. E equals HV, and we also have anot

¿Cuál es la longitud de onda (en metros) de los fotones con...

Key Concepts

Electromagnetic Spectrum Regions

The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation, with each region (such as ultraviolet, visible, infrared, etc.) corresponding to a specific wavelength interval. Identifying the region in which a photon lies involves comparing its calculated wavelength to the known wavelength bounds for each part of the spectrum.

Photon Energy-Wavelength Relationship

This concept is based on the fundamental equation E = hc/?, which relates the energy of a photon (E) to its wavelength (?) using Planck’s constant (h) and the speed of light (c). It is a central principle in quantum mechanics that explains how light behaves both as a wave and as discrete packets of energy (photons).

Energy per Mole Conversion

In many chemistry problems, energy is provided in kilojoules per mole instead of per individual photon. Converting energy from a per mole basis to a single photon basis requires dividing the given energy by Avogadro’s number, which is the number of entities in one mole. This conversion is essential for applying the photon energy-wavelength relationship accurately.

Transcript

00:01 Okay, to solve this, we are going to start with our equation.

00:06 E equals hv, and we also have another equation c equals lambda v.

00:13 So our lambda is our wavelength.

00:17 I'm just going to want to wave.

00:20 V stands for frequency.

00:29 Again, this would be frequency, and then h is planck's constant, which is 6 .6.

00:38 Times 10 to the negative 34.

00:43 Great.

00:44 So we want to rearrange e in order to have our wavelength in it.

00:49 So if we first rearrange this equation, oh, and c is the speed of light.

00:53 I'll just put sl, speed of light.

00:57 So we know that wavelength equals c divided by v.

01:10 Oh, you know what? excuse me, i just did something.

01:17 This is a better way to explain it.

01:18 Okay, we know that v equals c over wavelength.

01:28 And now we can go ahead and plug this v into our equation right here, and we will get e equals hc over wavelength.

01:41 You can also just memorize e equals hc over wavelength, but i think it's always helpful to kind of see where you would derive that.

01:48 Okay, so for the first one, we have 90 .5 kilojoules per mole.

01:59 So first we want to make sure we put everything into jewels.

02:03 So to do that, we're just going to multiply this by a thousand.

02:08 That'll give us jewels.

02:11 And then this is our energy, so it's going to be equal to planks, constant.

02:18 So 6 .6 times 10 to the negative 34th.

02:27 Great.

02:28 And then we have our speed of light, which is 3 times 10 to the 8th.

02:33 That's always something you should memorize.

02:37 And then in order to get rid of this moles, we want to multiply this by apagodro's number, which is 6 .02 times times 10 to the 23rd.

02:52 And i'm leaving my units out, but it's always good practice to put your units in as well.

02:58 And then we're going to have our wavelength here.

03:02 So again, this is just plugging in what we already know to this equation up here.

03:09 So if you go ahead and solve for that, you will find that wavelength equals 1 .32 times 10 to the negative 6 meters.

03:33 All right.

03:33 And then in order to find what this would correspond to in the electromagnetic spectrum, we had that here.

03:41 So we're going to find 10 to the negative 6th, which is right here...

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