General Chemistry Structure of Atoms

Hi, welcome back to Educator.com.0000

Today's lecture in general chemistry is going to be the structure of the atom.0002

Here is the lesson overview; we are first going to do a brief introduction.0009

Followed by the introduction, we are going to talk about something we call electromagnetic radiation.0015

Then we are going to get into the early model of the atom which was called the Bohr model.0021

We are then going to discuss what is called the wave nature of matter.0027

The core of this chapter is the currently accepted theory for the structure of the atom.0034

That is going to be what is called quantum mechanics.0041

One implication of quantum mechanics is that we get to visualize what are called atomic orbitals.0045

After that, we will go ahead and summarize, followed by a few sample problems.0055

Here is our introductory slide.0063

From previous lectures, we have talked about Earnest Rutherford's gold foil experiment.0066

If you recall, Rutherford was able to find that neutrons and protons existed inside the nucleus while electrons existed outside the nucleus.0072

That was a very important finding because we were able to come up with a positively charged center that is very dense.0086

Every atom has it, which we call the nucleus.0095

But then some questions immediately arose.0098

If electrons are outside the nucleus and protons are inside the nucleus, why don't they collide with each other?0103

Why don't electrons collide with protons and crash into the nucleus because opposite charges attract?0111

If this collision occurred, then the atom should itself collapse.0119

As you see, this structure of the atom was almost paradoxical.0126

It is a very good theory; but why doesn't the atom collapse?0140

At the time, there wasn't really anything that could explain for this paradox.0144

Before we get into more detail, we now have to discuss the electron and its relationship with light.0153

The light that we see as humans is a form of energy, what we call electromagnetic radiation.0166

Radiation can be pretty much characterized by three parameters.0174

Energy which we are going to symbolize with capital E.0178

Frequency which is going to be symbolized with the Greek symbol nu(ν).0181

Finally wave length which is going to be symbolized with the Greek symbol lambda(λ).0186

Energy, we have talked about energy before.0191

This is going to be usually in units of joules.0194

Frequency, it is like the frequency on your radio.0197

That is going to be in the units of hertz.0200

Hertz is the same thing as reciprocal seconds.0203

Finally wavelength, this is going to be usually in meters or nanometers.0207

Basically if we have a travelling wave, you can think of a sine or a cosine function.0218

We have a traveling wave.0224

The wavelength is just the distance between two adjacent peaks or two adjacent troughs.0226

Frequency is the rate at which a wave passes a specific point in time.0236

The higher the frequency, really you can think of it as the faster it is passing that same point in time.0244

What is the mathematical relationship between wavelength and light?--it is the following.0252

c is equal to λ times ν; it is equal to a constant.0258

This constant is something you will recognize; it is the speed of light.0263

The speed of light is approximately 3.0 times 10⁸ meters per second.0271

The important thing from this equation to remember is the proportionality relationship between wavelength and frequency.0279

As we see, they are inversely related; inversely proportional.0287

In other words, the longer the wavelength, the shorter or smaller the frequency.0293

Now that we have been introduced to the three parameters used to characterize electromagnetic radiation, let's now look at the different types of radiation.0302

The different types of radiation collectively is what we call the electromagnetic spectrum.0312

You will find this in any beginning physics course and general chemistry course.0320

Probably you have encountered this some time or another.0326

On the left side of the spectrum is what we have, the long wavelength value; this is long λ.0333

Remember because λ is inversely related to frequency, this means that this is small frequencies.0343

Another important relationship is the following; that energy is directly related to frequency.0353

Long λ, small frequency, also means small energy.0361

Right off the left end here is going to be the radio waves,0370

the same radio waves that we listen, that we use to listen to music, etc.0374

After radio waves is going to be microwaves; after microwaves is going to be infrared.0380

What infrared is, it is abbreviated IR; it is pretty much...0387

You can think of infrared as any type of heat that you feel coming from a warm object.0390

Then we get into the visible region.0397

This is the visible region that you and I as humans see.0400

As you can see, this is in the order of R-O-Y-G-B-I-V.0403

The colors of the rainbow are always in that specific order.0410

They are literally ordered by their energies.0413

In this case, red is going to be the weakest colored light in terms of energy.0417

Violet is going to be the greatest colored, the greatest energetic light in the visible region.0425

After visible comes ultraviolet; the UV light basically that comes from the sun.0439

After UV, we are getting into x-rays.0446

You can already tell, these are terms you recognize already from everyday language.0449

We are getting indeed more and more energetic.0454

Finally we finish it off with gamma rays.0456

Gamma rays is the type of energy that can be emitted from a nuclear power plant.0459

Now that we have studied the different types of electromagnetic radiation, we want to now try to relate it to the electron.0468

In order to do that, I need to now go over with you what happens when light passes through a prism.0479

When white light passes through a prism, we have all seen this.0486

It is separated into the different colors of the visible spectrum, and we essentially get the rainbow.0490

But that is white light; what happens when we do the following?0497

When we excite an element vapor, maybe with electricity, it turns out that the light that we see0501

as humans is not a rainbow but instead it is going to be specific colors of light.0510

In other words, it is different wavelengths unique to the element are emitted.0515

Sodium vapor, when it is excited, we get an orange light.0520

This is the same light that is used in residential street lamps.0525

It is the same color light that you see when hot water touches the blue flame on your stove.0529

It is because of sodium ions get excited in the water, giving off the same colored light, orange-yellow.0535

Xenon vapor, xenon vapor, sometimes you will see xenon being used in very nice expensive headlights on your car.0543

You can recognize that as a nice blue color, purple color.0555

The emission of light can be used as a fingerprint identification for elements.0560

In other words, different elements give off different colors or emit different colors.0568

Different elements give off different colors.0583

Why is this so?--why do elements give off different colors?0587

In order to do that, we are now going to introduce what was commonly accepted at the time for atom structure.0591

This is called the Bohr model of the atom.0597

Niels Bohr came up with a model as to why different elements give off different wavelengths of light.0600

Essentially you have the nucleus right at the middle.0608

You have what are called circular orbits around the nucleus.0613

Immediately you will recognize this as analogous to a solar system.0621

Not only is this called the Bohr model, this is also called the planetary model of the atom.0630

Basically there is a couple of things we want to remember.0643

Electrons which we know from Rutherford's experiment exist outside the nucleus.0646

They travel in these circular orbits around the nucleus.0651

The larger the orbit, the higher the energies.0657

Basically the farther out you go, the higher the energy.0659

Electrons can instantaneously transfer between orbits, but they cannot exist between.0664

They can exist in n equal to 1, n equal to 2, n equal to 3, but not in between.0672

Finally how did Bohr explain for light emission?0679

Basically energy is always going to be released in the form of light when an electron does the following.0683

As it falls from a higher energy to a lower energy level.0689

If we look right here, we have an electron going back to the n equal 1 level from equal 2.0694

Energy is going to be emitted in the form of light that you and I see.0704

We will write this as n equal 2 to a n equal 1 transition.0711

Once again energy is released in the form of light as you go from a higher energy to a lower energy level.0718

Or as you go from an outer orbit to an inner orbit; outer orbit to an inner orbit.0724

Again this is what we call the planetary model of the atom or Bohr's model.0737

The first element that we will study is of course going to be the simplest one.0745

This was hydrogen.0748

When hydrogen in the gas phase is excited, we can go ahead and take a look at the colors of light that are given off.0750

The Balmer series is commonly known; here I show it to you.0756

It shows four lines, each of a different color, in the visible region.0763

The technical term for these fine separate lines is what we call discrete.0769

This is what we call the Balmer series or hydrogen's photoemission spectrum.0776

Photo, it means light; emission means given off.0781

It turns out that we can come up with an equation that actually predicts the wavelength of light that is given off.0786

For hydrogen, this equation is what we call the Rydberg equation.0796

It is basically 1 over λ is equal to a constant R times the following.0802

1 over n₁ squared minus 1 over n₂ squared.0808

R is what we call the Rydberg constant.0813

It is equal to roughly 1.1 times 10⁷ reciprocal meters.0819

You should probably ask your instructor if you need to memorize this or not.0823

λ, this is going to be the wavelength in meters of the light that you and I detect with our eyes.0827

This is going to be in meters.0838

Again this is the wavelength of light that you and I detect that is given off.0840

1 is going to be equal to the initial energy level or orbit.0846

n₂ is going to be equal to the final energy level or the orbit.0859

This equation works remarkably well for hydrogen; the interesting to note is the following.0866

For this equation to work, the energy level of an orbit can never be equal to zero.0877

We cannot take 1 over 0 for example; the important implication is the following.0884

Because n can never be 0, electrons cannot exist inside the nucleus.0890

We answer the question, why doesn't the atom collapse?0898

Because using this mathematical equation, we cannot have an electron existing inside the nucleus.0902

Now that we have talked about atomic spectroscopy and photoemission,0914

we want to now get into a little more philosophical arguments0919

and the early work that has been done in quantum mechanics.0924

This is what we call the wave nature of matter.0929

Matter which of course includes electrons which traditionally viewed as behaving as particles.0933

This is coming from classical physics.0942

What we mean by particles, that means we can plot a trajectory.0949

We can come up with an equation for it basically.0954

The Bohr model came from classical physics.0957

It thought of electrons as travelling in these fixed circular trajectories around a nucleus.0961

However an interesting finding had occurred.0969

When you take a wave and you pass it through a very small slit,0974

you can capture the resulting image on a piece of photographic film.0988

What happens is you get an alternating pattern.0996

The beam is essentially going to split into such a pattern.1000

The dark area represents what we call destructive interference.1012

The other areas represent constructive interference.1023

Again this is all coming from physics.1028

Some of you may have had this already in your physics course.1030

Basically destructive interference is when two waves essentially cancel each other out.1035

Constructive interference is when the waves, their amplitudes are combined.1046

This is highly characteristic of any wave.1057

You get this alternating pattern between destructive and constructive interference when a wave has passed through a very narrow slit.1062

This experiment was then repeated with a beam of electrons.1073

When the beam of electrons passes through this very narrow slit, it turns out that you get the same pattern.1079

This is a highly interesting because we thought of electrons and matter as only behaving as particles.1091

But what this shows, this shows that electrons and therefore matter also has characteristics of a wave.1101

Matter has also wave-like characteristics; wave-like character in addition to having particle character too.1110

This term was what we call the wave particle duality of nature.1145

This early experiment pretty much helped to give rise to a new1154

school of thought early in the twentieth century and late nineteenth century.1160

Basically the new thought viewed matter as having both a wave and particle duality.1168

There were many famous well-known scientists whose names you are going to recognize1178

that helped to contribute to this new movement known as quantum mechanics.1183

Einstein described energy in what he called photons which were essentially discrete quantized packets of energy.1189

In addition to being described as a moving wave, photons he thought were described as tiny packets of energy, something like that.1207

Two more scientists were Hertz and Planck.1217

Hertz and Planck helped to describe what was called the photoelectric effect.1220

Basically when a metal absorbs energy, light can be emitted in the form of photons1225

having an energy E is equal to hν minus φ1232

where h is equal to Planck's constant and phi(φ) is what we call the threshold energy.1237

Basically it is literally the energy required to remove an electron from a metal surface.1249

Energy needed for electron removal from a metal surface.1261

Another scientist that came along was de Broglie.1276

He helped to develop an equation which gave the wave length of a moving particle.1279

Here we are finally being able to quantify the wave-like nature of matter.1283

Basically the wavelength of a moving particle is equal to λ which is equal to h over mv.1290

h is Planck's constant again.1298

m is going to be the mass of the particle but in units of kilograms.1300

Finally v is just your ordinary velocity in units of meters per second.1306

In this case, λ will be in units of meters then.1314

Again we were able to early on from these scientists' contributions,1320

quantify both the wave character and the particle character of matter.1327

Moving on, another important fundamental contribution to quantum mechanics was Heisenberg.1338

Heisenberg came along and developed his very groundbreaking what we call uncertainty principle.1346

He basically said the following.1354

That for a moving electron, we cannot simultaneously ever know both the position and the momentum.1356

Both the position and momentum of a moving electron can never be simultaneously known.1364

Instead only a probabilistic determination of a moving electron's position can be formulated.1370

What does that mean?--that means we can give a pretty good guess or1376

estimate of where an electron may be found, where it may occur around a nucleus.1382

Finally the next scientist was Schrödinger.1390

Schrödinger helped to develop the concept of what was called a wave function.1394

What a wave function is, it is a mathematical function that describes the energy of a moving particle with respect to time.1398

A wave function then, this is what we also call an atomic orbital.1407

An atomic orbital is basically a probability map of where an electron may occur around the nucleus.1408

A probability map of electron location around a nucleus.1427

Moving on, if we took a look at these wave functions, we will see that they will be somewhat complicated.1444

We are going to leave that for a upper division quantum mechanics course.1452

But what I want you to take away is the following.1458

If we were to solve the wave function and we were to look at these atomic orbitals1462

in more detail, the solutions contain what are called quantum numbers.1469

Basically there are four quantum numbers.1474

Number one is what we call the principal quantum number, n.1476

n describes the overall energy of an electron.1479

I want you to think back to the Bohr model of the atom.1484

We use lowercase n to describe each ring around a nucleus, each orbit.1486

It is pretty much the same thing.1491

As the energy level increases, so does the n value.1493

Please note, n cannot be 0.1498

n is only going to be a positive whole number, that is not zero.1500

The second quantum number is what we call the angular momentum quantum number.1506

This is going to be symbolized with lowercase l.1513

This is going to describe the shape of the atomic orbital.1516

Where in other words, if we take the wave function, this mathematical equation,1521

and we plot it in three-dimensional space, we get an image basically.1525

These images... we are going to take a look at it on the next slide... all have very characteristic shapes.1531

l, possible values are going to be 0, 1, 2, all the way up to and including n-1.1539

If l is equal to 0, the orbital designation is what we call an s orbital.1550

Again this is going to make more sense in a slide or two.1562

If l is equal to 1, we call the characteristic shape, a p orbital.1565

If l is equal to 2, we call the characteristic shape, a d orbital.1571

Finally if l is equal to 3, we call the characteristic shape of the wave function in three-dimensional space, an f orbital.1577

Moving on, the third quantum number is what we call the magnetic quantum number.1588

Magnetic quantum number is going to be symbolized with lowercase m_l.1593

It describes the spatial orientation of the wave function in three-dimensional space.1599

m_l will be equal to ?l all the way to 0 and then all the way to +l.1604

There is something important to make a note of.1614

If l is equal to 0, then m_l is just equal to 0.1618

l equal to 0 is an s orbital.1625

m_l is just equal to 0; that is only one value.1627

If l is equal to 1, then m_l can be equal to -1, 0, +1.1633

If l is equal to 2, m_l can be equal to -2, -1, 0, +1, and +2.1641

Finally if l is equal to 3, we get to -3, -2, -1, 0, +1, +2, and +3.1650

The reason why I am bringing this up is going to play a very big role in the next presentation.1660

But please make a note.1665

s orbitals, if you look at it, there is only one value of m_l.1667

That means there is only one s orbital per energy level.1671

What we are looking at is not the specific values of m_l, but the numbers, how many m_l values do we have.1682

For the p orbitals, -1, 0, 1, which means we are going to have three p orbitals per energy level.1691

For the d orbitals, there are five m_l values which means we are going to have five d orbitals per energy level.1702

Finally f orbitals, there are seven m_l values which means we are going to have seven f orbitals per energy level.1711

Finally the last quantum number is what we call the spin quantum number.1723

The spin quantum number is going to be symbolized with lowercase m_s.1728

Basically there is only two values, + or ? 1-1/2.1733

It describes the relative spin of an electron.1737

You can have either spin up or spin down.1741

We are going to be using that terminology a lot in the next presentation.1743

Those are the four quantum numbers that are used to characterize and describe an atomic orbital for an atom.1749

What do these atomic orbitals look like?1757

What do the wave functions when they are plotted in three-dimensional space look like?1760

There is two ways to go about this.1767

The first one is what we call the radio wave function.1769

When we do a radio wave function, it is basically describing electron density at different distances from the nucleus.1776

When we plot for example what we call a 3s orbital, this is going to be our zero line.1787

We are going to get graph that looks like that.1798

This zero line means zero electron density.1803

When we go ahead and look at a 3p orbital, we are going to get something like this.1811

Finally let's go ahead and look at 3d.1821

3d is going to go ahead and look like this.1826

We need a point of reference in order to compare it.1830

Because this is hard for us to look at this overlapped.1832

The point of reference is going to be the same on each of these graphs--here, here, and here.1835

What the x-axis is is the distance from the nucleus.1842

Basically let's examine the s orbital.1853

The s orbital tells us that there is quite a high density of electrons very close to the nucleus.1857

The p orbital tells us that we also have a good density of electrons close to the nucleus, but it is less than 3s.1866

Finally for 3d orbitals, the electron density is farther out from the nucleus.1875

This is very important.1882

The value of 3 is basically the value of n.1886

As you can see, as you go from s to p to d in the same n value,1891

basically the electron density is going to be very high farther and farther out.1903

In other words, the atomic orbital size is increasing; atomic orbital increases in size.1908

That is what we can take away from these radio wave functions.1922

Another way of plotting this is what we call the probability distribution function.1930

This is basically the probability, not electron density, but probability of finding an electron at a certain distance from the nucleus.1935

When we do it for 3s, we are now going to get a graph that looks like this.1944

We do it for 3p, we are going to get a graph that looks like that.1951

Finally for 3d, we are going to get something that looks like that.1957

Once again the y-axis is going to be probability.1963

The x-axis again is going to be distance from the nucleus.1968

What we want to point out here is the intercepts.1982

We want to point out the intercepts here.1988

These intercepts literally mean I have gotten zero probability of finding an electron that specific distance from the nucleus.1991

These are what we call radial nodes.2000

What a node is when we have zero probability at that point from the nucleus.2005

As you can see, this 3s orbital has two nodes, 3p has one node, 3d has zero nodes.2010

The simple equation predicts the number of radial nodes for the atomic orbital.2018

The number of radial nodes equals to n minus l minus 1.2023

These are the different ways of plotting wave functions.2039

But that is two-dimensional graphs.2043

What happens now when we plot it in a three-dimensional space?2046

This is what we typically show at this level of general chemistry.2050

You may have had this even in high school.2057

An s orbital, as you can see, how do you tell?2062

There is only m value; m_l value.2067

An s orbital is basically going to be a sphere.2070

A sphere therefore is going to have greatest density right at the center or close to the nucleus.2078

For these, we have three m_l values; remember we call that p orbitals.2086

p orbitals are also known as a dumbbell shape.2092

Basically those nodes are right at the middle.2099

We have electron density farther from the nucleus, not at the center.2105

Next one, here five of the m_l values.2111

These are there for the d orbitals; again you have nodes at the center.2117

Finally you have seven here m_l values; these are going to be the f orbitals.2128

What I want you to take away from this is that again as you go2135

from s to p to d to f, the orbital size increases which means you are going to2139

have a higher probability of finding an electron farther away from the nucleus.2147

Again these are the characteristic shapes of atomic orbitals.2154

Let's go ahead and summarize this presentation on the structure of the atom and quantum mechanics.2159

We first started off the presentation with a look at light.2166

We saw that light is a form of what we call electromagnetic radiation.2172

It can be described by energy, wavelength, and frequency.2176

The early model of the atom was the Bohr model or also known as the planetary model.2181

It gave a very simplistic view of photoemission which incorrectly assumed that electrons travelled in fixed circular orbits around the nucleus.2187

That is where quantum mechanics came in.2196

Quantum mechanics resulted from the idea that matter has both a wave particle nature.2198

Electrons don't travel in fixed orbits.2206

Instead we can only give a probable location of the electron.2208

This is coming from Heisenberg's uncertainty principle.2215

Finally Schrödinger helped to develop what were called wave functions which gave rise to concept of the atomic orbital.2219

Let's go ahead and tackle some sample problems right now.2227

The energy required to dislodge electrons from sodium metal via the photoelectric effect is 275 kilojoules per mole.2231

What wavelength in nanometers of light has sufficient energy per photon to dislodge an electron from sodium?2238

This is 275 kilojoules per mole; that is our energy.2246

We need to go from here to wavelength in energy per photon; maybe in kJ per photon.2258

Basically we are in kJ per mole right now.2269

We want to go to the wavelength of light that has enough energy to dislodge an electron from sodium.2272

This wavelength is going to be in meters.2288

When we look at 275 kilojoules per mole, we want to go to per photon.2294

That is going to be individual particles.2302

We are just going to use our Avogadro's number; divided by 6.022 times 10²³ photons.2304

That is going to give us 4.57 times 10^-22 kilojoules per photon.2315

We want to go from energy to wavelength.2325

This is going to be energy is equal to hν.2330

ν, this is going to be c over λ.2337

This is our Planck's constant equation basically.2345

That allows us to go from energy to frequency to wavelength.2350

But remember Planck's constant is 6.626 times 10^-34 joules times second.2354

Here we are in kilojoules; let's go ahead and get that to regular joules.2366

When we do that, we get 4.57 times 10^-19 joules per photon.2371

We are in good shape; we can plug everything directly into the equation.2379

When we do this first part, we can solve for frequency.2384

When we do that, frequency is going to be equal to the energy divided by h.2391

That gives us 6.9 times 10¹⁴ reciprocal seconds.2397

When we plug that into ν is equal to c over λ, we can go ahead and solve for λ.2403

We are going to get a wavelength of 435 nanometers.2412

435 nanometers is roughly violet blue light; that is one common sample problem.2418

Another sample problem, let's go ahead and look at it.2427

An electron in the n equals 6 level of the hydrogen atom relaxes to a lower energy level, emitting 93.8 nanometers of light.2430

What is the principal level to which the electron relaxed?2437

Relaxed is just a technical word for fall to.2440

This is involving the hydrogen atom and light that is emitted.2448

We are going to use the Rydberg equation.2452

1 over λ is equal to R times 1 over n₁ squared minus 1 over n₂ squared.2455

The wavelength of light that emitted is 93.8 nanometers, but we need to get that into meters.2465

That is going 1 over 9.38 times 10^-8 meters; that equals to R.2470

1.097 times 10⁷ reciprocal meters times 1 over n₁ squared.2478

The n equal to 6 is n₁; that is 6 squared.2488

What we are trying to solve for is where the electron fell back to--that is the final energy state.2493

When all is said and done, n₂ is equal to 1.2499

How do you know if you have done some miscalculation?2504

Remember n can only be a positive whole number.2506

If you get a really off number, has a lot of decimal places, you probably did something incorrectly.2510

This transition therefore is n equals 6 to n equal to 1.2521

It is going to give off a photon with a wavelength of 93.8 nanometers in hydrogen.2526

That is the structure of the atom and introduction to quantum mechanics.2535

Thank you for using Educator.com; I will see you later.2539