00:01
And we've got some information to get us started on this one.
00:04
It's going to be a bit of a long one.
00:06
So here, starting off, we've got the different equations we're going to use.
00:10
So this problem is giving us beginning and final n values or principal quantum values, and we're going to calculate the wavelength that would, in this case, the light is emitted in all of these situations.
00:24
We'll talk about as we go on.
00:26
So some of the information we need first, we need this first equation.
00:29
This has the change in energy between the two energy levels equals negative rh.
00:35
That's called the rydberg constant.
00:37
The h is actually a subscript.
00:39
Okay, so it's not r and then h.
00:41
It's that represents one thing.
00:44
Equals 1 over n final squared minus 1 over n initial squared.
00:51
So for each of these a, b, c, and d, they give us a transition.
00:55
In a, they tell us n equals 2 to n equals 1.
00:58
So our initial n, our n -i will be a 2.
01:03
Our n -final will be a 1.
01:06
Okay, and then those values will be squared.
01:08
There is a constant in there, the r -h, that r -h -that -r -berg constant.
01:11
I wrote it underneath in green.
01:14
Once we have the energy, then we need to work towards getting to wavelength.
01:20
There's a couple different ways you can do this.
01:22
The one i have is the simplest form.
01:24
It is a two -step problem, but it keeps the equation simple.
01:27
So first we'll use e equals hv, or that v is technically a new, a greek lettered new.
01:37
It represents the wavelength.
01:39
Normally when we use a v, we mean velocity and chemistry.
01:42
So they decide to use greek.
01:44
It represents the frequency.
01:48
E will be the energy we get from the first equation.
01:51
H is a constant.
01:52
It's called planx constant.
01:53
I wrote it there to this side, the 6 .66, 10 to the negative 34.
01:57
The units are joules times seconds.
02:02
And then lastly, once we have the frequency, we can get to the wavelength.
02:06
That's this last equation.
02:07
C equals lambda, new.
02:10
So again, we've got that greek letter new for the v, look in the guy.
02:14
And then we have got lambda.
02:16
This is another greek letter.
02:18
Lambda.
02:21
One of those should be a b.
02:22
The first one's a b.
02:24
There we go.
02:25
Let's fix that.
02:28
Lambda.
02:29
There we go.
02:30
Okay.
02:30
It is the wavelength, where the new was the frequency.
02:43
Okay, so a lot of steps.
02:45
Once we have those, it wants to know what part of the electromagnetic spectrum this falls on.
02:52
So that's where this image is that i have on the right hand side.
02:54
This is your electromagnetic spectrum.
02:56
The values, the numbers are written in terms of the wavelength.
03:01
And so this one just has a little pop out that shows you the visible range.
03:04
Underneath it, i wrote some of the typical ones, ultraviolet, visible, and infrared.
03:09
Okay.
03:10
Ultraviolet is energy is light that has a wavelength between 100 and 400 nanometers.
03:16
Now we don't want to have to convert our final wavelength into nanometers.
03:21
It's just an extra step.
03:23
So i decided to make this easier.
03:24
100 to 400 nanometers.
03:27
That's one times 10 to the negative 7 to 4 times 10 to the negative 7 meters.
03:32
So we'll look at our final answer to all these equations, see if it falls in that range.
03:37
Visible light is between 400 and 700 nanometers that would be four times 10 to the negative 7 to 7 times 10 to the negative 7 meters and then lastly infrared that's between 700 nanometers and one millimeter it's a much larger range that is 7 times 10 to the negative 7 meters to 1 times 10 to the negative 3 meters so a much larger range if we have wavelengths that fall out of this category, we can look at the other things on there, like radio waves or x -rays.
04:16
But in this case, they all fall into one of these three categories.
04:19
So we'll keep it simple.
04:21
Okay.
04:22
I'll walk you through step by step through these.
04:24
The first time through for a, i'll take a little bit more time to explain every little detail.
04:28
And then b, c, and d will go through fairly quickly because they're all the same steps.
04:33
But i'll put all the numbers down so that you have something to compare to if you're struggling.
04:37
All right so for part a we are going from n equals 2 to n equals 1 all right that means 2 is our initial final and 1 is going to be our final all right our change in energy is negative r h which is negative 2 .18 times 10 to the negative 18 jules times 1 over and final squared so that would be 1 squared minus 1 over an initial squared.
05:21
So here's our equation to start with.
05:23
We'll do what's in the parentheses first.
05:26
So 1 over 1 squared, that's just 1, right? because 1 squared's 1, and then 1 over 1 is just 1.
05:32
So we've got 1 minus 1 over 2 squared.
05:38
Okay, that would be minus 1 over 4.
05:42
Plug that into your calculator and i get negative 2 .18 times 10 to the negative 18 joules and then the parentheses come out as what did i get for that 0 .75 i got to get the final energy multiply the negative 2 .18 10 to the negative 18 by 0 .75 and you get negative 1 .635 times 10 to the negative 18 and the units we've got in here going are jewels so this will be in jewels all right so that's our change in energy that's the first equation done next we go into the next one which was the e equals hv right now this e equals hv equals h new however you want to say it is fine new is the correct way for frequency we have it written as i write this off to the side e equals h new like this what we're interested of that, we want the frequency.
06:57
So if you wanted to get that new by itself, you would divide both sides by h.
07:02
So the equation we're really working with is e over h equals new.
07:12
So here we go.
07:15
E over h.
07:16
So the delta e came out as a negative value.
07:20
Correct.
07:20
We had negative 1 .635.
07:23
The negative value is telling you the direction.
07:26
If it's a negative value, think about if you've done enthalpy before now, where you could have endothermic or exothermic, where an endothermic value was positive.
07:36
It meant something was being added to the system.
07:39
Exothermic meant exit means leaving.
07:42
So that meant something was leaving.
07:44
Those are negative values.
07:45
The same thing applies here.
07:46
A negative wavelength simply means that that is energy that is leaving the system, which in this case is the hydrogen atom.
07:55
When we went from the second to the first energy level, energy was released as light, and its wavelength was 1 .635, 10 to the negative 18.
08:06
It's energy.
08:07
I'm sorry, not it's wavelength, it's energy.
08:10
Okay.
08:10
So that negative sign, we don't, we use it with energies, but we don't use the negative sign with a wavelength or frequency.
08:16
So we're actually going to drop that negative sign and just take the 1 .635, 10 to the negative 18.
08:24
So we're doing the e over h.
08:27
So that is 1 .635, 10 .10.
08:31
10 to the negative 18 joules divided by h, which was that constant.
08:36
We wrote it up at the top, 6 .626, 10 to the negative 34, joules times seconds.
08:45
Unit -wise, our jewels are going to cancel.
08:49
And we're going to end up with seconds in the denominator.
08:54
And i get 2 .468, 10 to the positive 15th, with the units of 1 over seconds.
09:05
Okay, one over seconds can be written a couple ways.
09:08
It can be written as one divided by seconds, or seconds to the minus one power.
09:15
Anytime you have a minus one power on something, it just means put it in the denominator, so that means the same thing.
09:21
Or you might even see hertz, which is hz.
09:24
These all mean the same thing.
09:26
They just mean one over seconds.
09:28
They're used in different situations just to make it easier.
09:31
Okay, like if you're typing something, seconds to the minus one might be easier.
09:35
To type, so you're more commonly seeing that in textbooks.
09:40
Teachers tend to just choose whichever one that they're used to, but they all mean the same.
09:44
Okay, so this is our new.
09:47
This is our frequency.
09:49
Lastly, we want to get our wavelength...