For more information, please see full course syllabus of General Chemistry

For more information, please see full course syllabus of General Chemistry

### Related Articles:

### Structure of Atoms

- Light is a form of electromagnetic radiation which can be described by its energy, wavelength, and frequency.
- The Bohr Model, which gives a simplistic view of photoemission, incorrectly assumed that electrons traveled in fixed, circular orbits around the nucleus.
- The advent of quantum mechanics resulted from the idea that matter has both a wave-particle nature.
- Heisenberg’s Uncertainty Principle states that we can never know the exact location of a moving electron.
- Schrodinger helped develop wavefunctions, giving rise to the concept of the atomic orbital.

### Structure of Atoms

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro
- Lesson Overview
- Introduction
- Electromagnetic Radiation
- Electromagnetic Radiation
- Atomic Spectroscopy and The Bohr Model
- Atomic Spectroscopy Cont'd
- Atomic Spectroscopy Cont'd
- The Wave Nature of Matter
- The Wave Nature of Matter
- New School of Thought
- Einstein: Energy
- Hertz and Planck: Photoelectric Effect
- de Broglie: Wavelength of a Moving Particle
- Quantum Mechanics and The Atom
- Quantum Mechanics and The Atom
- The Shapes of Atomic Orbitals
- The Shapes of Atomic Orbitals
- Summary
- Sample Problem 1
- Sample Problem 2

- Intro 0:00
- Lesson Overview 0:07
- Introduction 1:01
- Rutherford's Gold Foil Experiment
- Electromagnetic Radiation 2:31
- Radiation
- Three Parameters: Energy, Frequency, and Wavelength
- Electromagnetic Radiation 5:18
- The Electromagnetic Spectrum
- Atomic Spectroscopy and The Bohr Model 7:46
- Wavelengths of Light
- Atomic Spectroscopy Cont'd 9:45
- The Bohr Model
- Atomic Spectroscopy Cont'd 12:21
- The Balmer Series
- Rydberg Equation For Predicting The Wavelengths of Light
- The Wave Nature of Matter 15:11
- The Wave Nature of Matter
- The Wave Nature of Matter 19:10
- New School of Thought
- Einstein: Energy
- Hertz and Planck: Photoelectric Effect
- de Broglie: Wavelength of a Moving Particle
- Quantum Mechanics and The Atom 22:15
- Heisenberg: Uncertainty Principle
- Schrodinger: Wavefunctions
- Quantum Mechanics and The Atom 24:02
- Principle Quantum Number
- Angular Momentum Quantum Number
- Magnetic Quantum Number
- Spin Quantum Number
- The Shapes of Atomic Orbitals 29:15
- Radial Wave Function
- Probability Distribution Function
- The Shapes of Atomic Orbitals 34:02
- 3-Dimensional Space of Wavefunctions
- Summary 35:57
- Sample Problem 1 37:07
- Sample Problem 2 40:23

### General Chemistry Online Course

I. Basic Concepts & Measurement of Chemistry | ||
---|---|---|

Basic Concepts of Chemistry | 16:26 | |

Tools in Quantitative Chemistry | 29:22 | |

II. Atoms, Molecules, and Ions | ||

Atoms, Molecules, and Ions | 52:18 | |

III. Chemical Reactions | ||

Chemical Reactions | 43:24 | |

Chemical Reactions II | 55:40 | |

IV. Stoichiometry | ||

Stoichiometry I | 42:10 | |

Stoichiometry II | 42:38 | |

V. Thermochemistry | ||

Energy & Chemical Reactions | 55:28 | |

VI. Quantum Theory of Atoms | ||

Structure of Atoms | 42:33 | |

VII. Electron Configurations and Periodicity | ||

Periodic Trends | 38:50 | |

VIII. Molecular Geometry & Bonding Theory | ||

Bonding & Molecular Structure | 52:39 | |

Advanced Bonding Theories | 1:11:41 | |

IX. Gases, Solids, & Liquids | ||

Gases | 35:06 | |

Intermolecular Forces & Liquids | 33:47 | |

The Chemistry of Solids | 25:13 | |

X. Solutions, Rates of Reaction, & Equilibrium | ||

Solutions & Their Behavior | 38:06 | |

Chemical Kinetics | 37:45 | |

Principles of Chemical Equilibrium | 34:09 | |

XI. Acids & Bases Chemistry | ||

Acid-Base Chemistry | 43:44 | |

Applications of Aqueous Equilibria | 55:26 | |

XII. Thermodynamics & Electrochemistry | ||

Entropy & Free Energy | 36:13 | |

Electrochemistry | 41:16 | |

XIII. Transition Elements & Coordination Compounds | ||

The Chemistry of The Transition Metals | 39:03 | |

XIV. Nuclear Chemistry | ||

Nuclear Chemistry | 16:39 |

### Transcription: 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 10 ^{8} 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 see *0501

*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 n _{1} squared minus 1 over n_{2} squared.*0808

*R is what we call the Rydberg constant.*0813

*It is equal to roughly 1.1 times 10 ^{7} 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

*n _{2} 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 arguments*0919

*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 new*1154

*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 recognize*1178

*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 photons*1225

*having an energy E is equal to hν minus φ*1232

*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 or*1376

*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 orbitals*1462

*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 go*2135

*from s to p to d to f, the orbital size increases which means you are going to*2139

*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 10 ^{23} 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 10 ^{14} 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 n _{1} squared minus 1 over n_{2} 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 10 ^{7} reciprocal meters times 1 over n_{1} squared.*2478

*The n equal to 6 is n _{1}; 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, n _{2} 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

0 answers

Post by Mahsa Khallaghi zadeh on September 22, 2015

I don't know how to solve this!

A ground state H atom absorbs a photon of wavelenght 104.54nm,and its electrons attain a higher energy level. the atom then emits two photons: one photon of wavelength 235nm to reach an intermediate energy level and the second photon to return to the ground stat.what intermediate level did the electron reach?