Chapter 4 electrons in atoms

Chapter 4: Electrons in Atoms This chapter is about electrons in the atom- a tricky subject at best- and the evolution of the atomic model. This chapter covers much material, some of it very difficult and abstract. It is essential that you bring your book to class and do all assigned homework.

Chapter 4 : Arrangement of Electrons in Atoms Atomic Models: - already discussed atomic structure – what was it? - inadequate – describes only a few properties of atoms - need a model that is focused on arrangement of ____, the basis of chemistry

Rutherford Model of the Atom The Rutherford Model (aka the Planetary Model) was an improvement over the previous models, but it was still incomplete. It did not include the distribution of the negatively charged electrons in the atom. We know that negative and positive particles (that is e - and p + ) attract each other, so the big question became: Why don’t the electrons crash into the nucleus ?

If + and – charges attract, why don’t e - collapse into the nucleus? In 1913, a student of Rutherford’s created a new model for the atom; he proposed the e - ’s were arranged in concentric circles around the nucleus (patterned after the movement of planets around the sun): The Planetary Model Along with this, he stated that the e - ’s have fixed energy that allows them to avoid falling into the nucleus, analogous to the rungs of a ladder. More on this later.

The Planetary Model of the Atom

But first, let’s talk about: The Properties of Light Before 1900, scientists thought light behaved solely as a wave. What idiots! It was soon discovered that light also has particle characteristics . But let’s first review the wavelike properties. The Electromagnetic Spectrum

The electromagnetic spectrum shows all the types of electromagnetic radiation - a form of energy that exhibits wavelike behavior as it travels through space. All forms of electromagnetic radiation move at a constant speed of 3.00 x 10 8 m/s through a vacuum. This is about 186,000 miles/s. Also known as the speed of light .

Let’s talk about waves and wave motion for a minute: Frequency and wavelength are mathematically related. This relationship is: c = λ v

c = λ v In the equation, c is the speed of light (in m/s), λ is the wavelength of the electromagnetic wave (in m), and v is the frequency of the electromagnetic wave (in s -1 or Hz). Important : λ and v are inversely proportional , so as the wavelength of light increases, the frequency decreases and vice versa. Practice Problems Determine the frequency of light whose wavelength is 4.257 x 10 -5 m. 2. Determine the wavelength ( λ ) of a photon whose frequency is 3.55 x 10 17 s -1 .

The Photoelectric Effect The photoelectric effect is a phenomenon that refers to: the emission of electrons from a metal when light shines on the metal. You’re most likely thinking: who cares? Well, here’s the thing- for any given metal, no electrons were emitted if the light’s frequency were below a certain minimum. Metal Light Electrons

The Photoelectric Effect (cont’d) So, obviously, light was known to be a form of energy , capable of knocking electrons loose from metal. But (important): the wave theory of light predicted that any frequency of light could supply enough energy to eject an electron, so the fact that there had to be a minimum frequency for a given metal made no sense. Something about the assumption of light behavior was wrong . Metal Light Electrons

The Particle Description of Light The German physicist Max Planck came up with the idea that light is emitted in small packets called quanta . A quantum of energy is the minimum quantity of energy that can be gained or lost by an atom. Here is the relationship between quantum and frequency of radiation: E = hv Where E is the energy (J), v is the frequency (s -1 ), and h is the physical constant called Planck’s Constant ; h = 6.626 x 10 -34 J · s S’up.

The Particle Description of Light In 1905, Einstein took this idea further by stating that light can act as both a wave and a stream of particles . Each particle of light carries a quantum of energy and is called a photon . A photon is a particle of electromagnetic radiation having zero mass and carrying a quantum of energy. E photon = hv Einstein was able to explain the photoelectric effect this way. Different metals bind their electrons differently, so v changes.

The Hydrogen-Atom Line-Emission Spectrum When an electric current is passed through a gas sample at low pressure, the potential energy of the gas changes. The ground state of an electron, the energy level it normally occupies, is the state of lowest energy for that electron. There is also a maximum energy that each electron can have and still be part of its atom. Beyond that energy, the electron is no longer bound to the nucleus of the atom and it is considered to be ionized. When an electron temporarily occupies an energy state greater than its ground state, it is in an excited state . An electron can become excited if it is given extra energy, such as if it absorbs a photon , or packet of light , or collides with a nearby atom or particle.

The Hydrogen-Atom Line-Emission Spectrum So what does this mean ? Well, when scientists passed an electric current through a vacuum tube with a pure gas in it (like H or O), each atom would go through the steps listed above: they would gain energy, and then reemit it in the form of a photon or light . This light was then passed through a prism , and the wavelengths (colors) in that element could be seen. Electrons do not stay in excited states for very long – they soon return to their ground states, emitting a photon with the same energy as the one that was absorbed.

The Hydrogen-Atom Line-Emission Spectrum So let’s use the example of helium. A tube of helium has a current of electricity pass through it, and the absorbed energy is then released in the form of light, thus, the tube glows. That light is then passed through a prism, which separates all the colors (wavelengths) in that light. Helium has a particular emission-spectra , or set of lines at specific color spectra. Every element has a signature color spectra .

The Hydrogen-Atom Line-Emission Spectrum But why are there only some colors appearing and not all of them? Because the electrons in these atoms have specific fixed energy levels , and only give off certain colors when jumping from level to level. Whenever an excited helium atom falls to its ground state or to a lower-energy excited state, it emits a photon of radiation. The energy of this photon ( E photon = hv ) is equal to the difference in energy between the atom’s initial state and it’s final state. Because different atoms have different energy levels, different atoms give off different frequencies (colors) of light.

The Bohr Model of the Hydrogen Atom Niels Bohr , scientist extraordinaire, solved the puzzle of why different atoms give off different color spectra. He linked the atom’s electrons to photon (color spectra) emission. According to his new model, electrons can only circle the nucleus in allowed paths, or orbits . Notice this!

The Bohr Model of the Hydrogen Atom (cont’d) When energy is added to an atom, the electrons move up energy level(s). Conversely, when energy is given off by an atom (in the form of a photon), the electrons move down one or more energy levels. The principal quantum number is denoted with the letter n , and it indicates the main energy level occupied by the electron. As n increases, the electron’s energy and it’s average distance from the nucleus increases.

Plotting the Electron “Orbit” It would be inaccurate to say that the electrons orbit the nucleus in the same way the planets orbit the sun, i.e., in a fixed and set path. The Heisenberg Uncertainty Principle states that you can know the position and velocity of an electrons at any given point, but never both at the same time. So if you were to plot the position of an electron many, many times, you would begin to build a picture of where it occupies space 90% of the time. This is called an orbital .

Plotting the Electron “Orbit” Orbital : the probable location of an electron around the nucleus. As n increases, the number of different types of orbitals increases as well. At n = 1 , there is one type of orbital; at n = 2 , there are two types of orbitals; and so on. The number of orbitals at any given energy level is equal to the principal quantum number ( n ). These are known as sublevels .

Types of Orbitals 1. s-orbitals : s-orbitals are spherical in shape, representing a hollow ball where you can find the electron 95% of the time. They are labeled 1-s, 2-s and so on to denote how close they are to the nucleus.

Types of Orbitals (cont’d) 2. p-orbitals : At the 1 st energy level, the only orbital available to the electrons is the s-orbital. But at the 2 nd energy level- after the 2-s orbital- there is the 2-p orbital. The p-orbitals are dumbbell shaped to represent where the electron can be found 95% of the time. Notice that near the nucleus, the area where they are usually found is very narrow.

Types of Orbitals (cont’d) 2. p-orbitals (cont’d) : unlike s-orbitals, p-orbitals point in a particular direction. At any one energy level it is possible to have three absolutely equivalent p orbitals pointing mutually at right angles to each other. These are arbitrarily given the symbols p x , p y and p z . This is simply for convenience - what you might think of as the x, y or z direction changes constantly as the atom tumbles in space.

Types of Orbitals (cont’d) 3. d-orbitals : after the s and p orbitals, there is another set of orbitals which becomes available for electrons to inhabit at higher energy levels. At the third level, there is a set of five d orbitals (with more complex shapes names) as well as the 3s and 3p orbitals (3px, 3py, 3pz). At the third level there are a total of nine orbitals altogether. 3d yz 3d xz 3d xy 3d z 2 3d x 2 -y 2

“Rungs of a ladder” N Energy of e- increases as you travel further away from the nucleus. e- can jump from energy levels when they gain/lose energy Quantum = amount of energy req’d to move an e- from its present energy level to the next highest; “quantum leap” Unlike a ladder, levels are not evenly spaced; closer further away thus easier to move b/t or leave.

The Quantum Mechanical Model (QMM) This is the most modern description of e - in an atom; it is purely mathematical and describes the _____ and _____ of an e - . All previous models differed b/c they were _______. This model doesn’t define an exact path of an e-, rather the QMM does what? “ Chance”

QMM = probability of finding an e- within a certain volume surrounding the nucleus; represented by an electron cloud The > probability of finding an e- is within these areas surrounding the nucleus ( represent where the e- is 90% of the time ). N The “fatter” the area of the e- cloud, the greater the chance of finding an e- and vice versa.

Atomic Orbitals Designate energy levels that e - are in by using principal quantum numbers (n) n is ordered from lowest  highest energy level (1,2,3,4…); thus the higher the principal quantum # the further the e - is from the nucleus. i.e.) an e - in the 3 rd principal energy level has more ___ and is further from the ___ than an e - in the 2 nd principal energy level. n =1 n = 2 n = 3 n = 4 ↑ energy, ↑ distance from nucleus, ↓ spacing N

Within each energy level there are sublevels ; the # of sublevels equals the principal energy level (n) The sublevels are also arranged from lowest to highest energy These sublevels have orbitals within them; each orbital can hold a max of 2 e- 3 sublevels n = 3 2 sublevels n = 2 1 sublevel n = 1 # of sublevels in that level Principal energy level (n) 7 orbitals 4 th = f 5 orbitals 3 rd = d 3 orbitals 2 nd = p 1 orbital 1 st = s # of orbitals within each sublevel Sublevels (lowest  highest energy)

Do Now: Discuss points you have learned about the PT: a. What does it tell us? b. How can we use it to talk about an element and its characteristics? c. How and why do we use the Aufbau Diagram? Homework: Finish electron configuration sheet; QUIZ Bring all lab materials tomorrow…

Basically… Principal energy level (n)  Energy sublevels  Orbitals in sublevels n = 1, 2, 3, 4… s, p, d, f, g … s =1; p = 3; d = 5; f = 7 (2 e-; 6 e-; 10 e-; 14 e-) QMM describes an e - position within an e - probability cloud; e - don’t travel in fixed circular paths, therefore we cannot call them orbits. Rather, we call them atomic orbitals ( s, p, d, f, g …)  SHAPES OF ATOMIC ORBITALS DICTATE PROBABILITY!!! s orbital p orbital (x 3) d orbital (perpendicular orbital coming at you; x 5) Fig 13.4, 5 in book Low to High

Another representation of the atomic orbitals… Clouds/”bubbles” indicate where you’ll find e- most of the time!

Notice w/ p and d orbitals the regions close to the nucleus where probability of finding an e- is very narrow = node Again, the # and types of atomic orbitals depends on what? Example: lowest principle energy level is n = 1; it has 1 atomic orbital called 1s Does the probability of finding an e- vary with direction in 1s? Does the same hold true for p and d orbitals?

The 2 nd energy level ( n = 2 ) has 2 sublevels, s and p. N P P P P P Coming @ you Going away from you 3.) Spaces represent what? P S 2.) How many total orbitals are there? What are the max # of e- that can be held in n= 2? 1.) P orbitals stick out further therefore they have > ____?

The 3 rd principal energy level ( n = 3 ) has how many orbitals? Can you name them? What is the max # of e- this energy level can hold? The 4 th principal energy level ( n = 4 ) has how many orbitals? Can you name them? What is the max # of e- this energy level can hold?

As mentioned, the principal quantum # always equals the # of sublevels in that energy level The max # of e- that can occupy a principal energy level is given by the formula… 2n 2 What is the max # of e- in the 6 th principal energy level? Sublevels? Still confused? Review p. 366 for max e- per energy level

Homework Electron configuration worksheet (work on wkst.) Have homework out to go over… Do Now: What is the Aufbau Diagram? How do you create it? What does it tell about filling orbitals? (use book to help you out) What is the total # of e- in n = 9? n = 5? What does the quantum # tell you?

Electron Configurations Natural phenomena to work towards stability – lowest possible energy WHY? High energy systems are very unstable Atom works to attain the most stable e- configuration possible

There are 3 rules that help you to determine this: Aufbau Principle Pauli Exclusion Principle Hund’s Rule 1 s 2 s 2 p Long form vs. Short form? Electron Configurations/Aufbau Diagrams

1) Aufbau principle : Electrons enter orbitals of lowest energy first . The various sublevels of a principle energy level are always of equal energy. Furthermore, within a principle energy level the s sublevel is always the lowest-energy sublevel. Each box represents an atomic orbital. Aufbau Diagram

2) Pauli exclusion principle : An atomic orbital may describe at most two electrons. For example, either one or two electrons may occupy an s orbital or p orbital. A vertical arrow represents an electron and its direction of spin ( ↑ or ↓). An orbital containing paired electrons is written as ↑↓ . 3) Hund’s Rule : When electrons occupy orbitals of equal energy, one electron enters each orbital until all the orbitals contain one electron with parallel spins. For example, three electrons would occupy three orbitals of equal energy as follows: ↑ ↑ ↑ Second electrons then add to each orbital so their spins are paired with the first electrons.

Some practice : ____ 5s ___ ___ ___ 4p ___ ___ ___ 4d ___ ___ Element

Electron Configuration This is the order which electrons will fill their energy levels: You MUST learn this!

Electron Configuration (cont’d)

Noble Gas Configurations A much easier way to write electron configurations, abbreviates all the orbital notation. This is an acceptable way to write electron configurations on quizzes or tests.

Show the electron configuration of the following elements: 1) Fe: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 6 2) Ga: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 1 3) Ar: 1s 2 2s 2 2p 6 3s 2 3p 6 4) Sr: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 5) Mg: 1s 2 2s 2 2p 6 3s 2 6) Ru: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 6

Homework Have worksheets out to quickly review questions (13.1 and 2) Complete 13.3, #1,2, 4, 6 (on loose-leaf, neatly, showing equations used, all work and cancellations in a vertical fashion ); will go over next session; use p. 375 example to help Do Now: Starting form n = 1 (to n = 4), list the order that electrons would fill sublevels… Quickly list and discuss all three rules for e- configuration discussed previously…

Take Quiz – 7 minutes Do Now: What is the difference between an atom and its ion? What is a node? Why is it unnatural for systems/atoms to be at high energy? How do atoms fix this problem? Homework – Complete chapter 13 worksheet (1 st page, front and back on the worksheet)

Physics and the QMM QMM developed through study of light Through its study, found light was energy that contained _____ and moved by ____.

According to the “wave model”, light consists of electromagnetic waves Includes… All waves travel in a vacuum at 3.0 x 10^10 cm/s (or 3.0 x 10^8 m/s)  = ? I’m smarter than he is? How’d he measure that?

Anatomy of a Wavelength origin amplitude Λ = “lambda” Frequency ( ν ) = “nu” = # of wave cycles that that pass through a point in a given time = Hertz (Hz) or s^-1 Wavelength and frequency are inversely related! Which leads us to…

Take 3 minutes only for quiz – hand in when finished. Do Now: Give the basic anatomy of a wavelength. What do we broad term describes all forms of light? Which portion makes up the smallest portion of this “spectrum”? How are wavelength and frequency related? Do they relate to anything else? Have essays and homework questions ready! Homework: Massive quiz on Monday (in lab) on all ch. 13 Remember to bring notebooks to class. Tuesday – Print out a PT and after reading chapter 14, create a “map” of how to interpret the periodic trends

ν “times” λ = speed of light Every time! Light bends through prisms to create the… Electromagnetic Spectrum = relative size?

Every element bends light in a specific way… Open book and complete sample 13.2 and practice problem 11

Another idea that came about through the study of light… The color change associated with the heating/cooling of an object occurs through the +/- of energy units = “bricks of a wall” Large energy change = emission/abs. of high frequency radiation and vice versa… thus, frequency and Planck’s constant are? E (“radiant energy”)= frequency x Planck’s constant E = ? Problem 13 on page 379

Chapter 4 electrons in atoms

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Chapter 4 electrons in atoms