Atomic Structure and Periodicity. AP Chemistry Ms. Grobsky

Transcription

1 Atomic Structure and Periodicity AP Chemistry Ms. Grobsky

2 Food For Thought Rutherford s model became known as the planetary model The sun was the positivelycharged dense nucleus and the negatively-charged electrons were the planets

3 The Planetary Model is Doomed! The classical laws of motion and gravitation could easily be applied to neutral bodies like planets, but NOT to charged bodies such as protons and electrons According to classical physics, an electron in orbit around an atomic nucleus should emit energy in the form of light continuously (like white light) because it is continually accelerating in a curved path Resulting loss of energy implies that the electron would necessarily have to move close to the nucleus due to loss of potential energy Eventually, it would crash into the nucleus and the atom would collapse!

4 The Planetary Model is Doomed! Electron crashes into the nucleus!? Since this does not happen, the Rutherford model could not be accepted!

5 How did Scientists Study the Structure of an Atom when They Couldn t Physically See It? Atomic structure was often elucidated by interaction of matter with light James Maxwell developed a mathematical theory to describe all forms of radiation in terms of wave-like electric and magnetic fields in space in 1864 Classical wave theory of light described most observed phenomenon until about 1900

6 But What Exactly is Light? Light is a form of ELECTROMAGNETIC RADIATION A form of energy that exhibits wavelike behavior as it travels through space Does not require a medium to travel through In a vacuum, every electromagnetic wave has a velocity (speed) of 3.00 x 10 8 m/s, which is symbolized by the letter c

7 Video Time! Electromagnetic Spectrum

8 The Electromagnetic Spectrum Electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation The highest energy form of electromagnetic waves is gamma rays and the lowest energy form is radio waves

9 Relationship of EM Wave Properties

10 Some Properties of Waves Wavelength (λ) Distance between two consecutive peaks or troughs in a wave Measured in meters (SI system) Frequency (ν) Number of waves that pass a given point per second Measured in hertz (sec-1) Speed ( c ) Measured in meters/sec Amplitude (A) Distance from maximum height of a crest to the undisturbed position

11 Relationships of EM Wave Properties Wavelength and frequency are related via the speed of light in a vacuum (c) c = 3.00 x 10 8 m/s Speed of light in a vacuum is a constant c = λ ν ALL ELECTROMAGNETIC RADIATION TRAVELS AT THIS SPEED! Therefore, wavelength and frequency of light are inversely proportional to each other As wavelength increases, frequency decreases As wavelength decreases, frequency increases

12 What s the Matter with Light?

13 The Nature of Matter By the end of the 19 th century, physicists were feeling rather smug They thought that all of physics had been explained and that matter and energy were two distinct entities: Matter was a collection of particles Energy was a collection of waves

14 The Ultraviolet Catastrophe There was a consistent observation of matter that could NOT be explained with the classical wave theory of light Elements in solid form glow when they are heated Do not emit UV light as predicted

15 Enter Max Planck Around the year 1900, a physicist named Max Planck was studying the energy given off by heated objects until they glow Planck solved the Ultraviolet Catastrophe with an incredible assumption: There is a minimum amount of energy that can be gained or lost by an atom All energy gained or lost must be some integer multiple, n, of that minimum as opposed to just any old value of energy being gained or lost

16 Planck and Quanta Planck called these restricted amounts of energy quantum No such thing as a transfer of energy in fractions of quanta Only whole numbers of quanta To understand quantization, consider walking up a ramp versus walking up the stairs For the ramp, there is a continuous change in height whereas up stairs, there is a quantized change in height

17 More on the Idea of Quanta Mathematically, quantum (packet) of energy is given by: h = Planck s constant = x J s ν is the lowest frequency that can be absorbed or emitted by the atom

18 Planck s Constant Planck s constant, h, is just like a penny Planck determined that all amounts of energy are a multiple of a specific value, h This is the same as saying that all currency in the US is a multiple of the penny

19 More Problems with the Wave Theory of Light

20 And then there was a problem In the early 20 th century, several other effects were observed which could not be understood using the wave theory of light The Photo-Electric Effect Every element emits light when energized either by heating the element or by passing electric current through it Elements in gaseous form emit light when electricity passes through them

21 What is the Photoelectric Effect? Electrons are attracted to the (positively charged) nucleus by the electrical force In metals, the outermost electrons are not tightly bound, and can be easily liberated from the shackles of its atom It just takes sufficient energy If light was really a wave, it was thought that if one shined light of a fixed wavelength on a metal surface and varied the intensity (made it brighter and hence classically, a more energetic wave), eventually, electrons should be emitted from the surface

22 Photoelectric Effect Classical Method Increase energy by increasing amplitude electrons emitted? No No No No What if we try this? Vary wavelength, fixed amplitude electrons emitted? No Yes, with low KE Yes, with high KE No electrons were emitted until the frequency of the light exceeded a critical frequency, at which point electrons were emitted from the surface! (Recall: small l large n)

23 Light as a Particle Einstein s Theory Einstein used Planck s idea of energy quanta to understand the photoelectric effect Proposed that EM radiation itself was quantized Light could be viewed as a stream of particles called photons Each photon carries an amount of energy that is given by Planck s equation

24 Einstein s Theory of Quantized Light E photon = hν = hc λ

25 Einstein s Particle Theory of Light You know Einstein for the famous E = mc 2 This equation shows that energy has mass??? Blasphemy! Rearranging this equation and substituting in Planck s equation: m = E c 2 = hc/λ c 2 = h cλ So, does a photon has mass? Yep! In 1922, Arthur Compton performed experiments involving collisions of X-rays and electrons that showed photons do exhibit the apparent mass calculated above!

26 Back to the Photoelectric Effect The light particle must have sufficient energy to free the electron from the atom Increasing the amplitude is simply increasing the number of light particles, but its NOT increasing the energy of each one! However, if the energy of these light particle is related to their frequency, this would explain why higher frequency light can knock the electrons out of their atoms, but low frequency light cannot Photoelectric Effect Animation

27 A Summary of Light as a Waveicle Light travels through space as a wave Light transmits energy as a particle Each photon carries an amount of energy that is given by Planck s equation E photon = hν = hc λ

28 So is Light a Wave or a Particle? On macroscopic scales, we can treat a large number of photons as a wave When dealing with subatomic phenomenon, we are often dealing with a single photon, or a few In this case, you cannot use the wave description of light It doesn t work!

29 The Dualism of Light Dualism is not such a strange concept Consider the following picture Are the swirls moving, or not, or both?

30 Time for Practice! Gallery Walk!

31 But How is This Related to the Atom?

32 Atomic Spectroscopy and the Bohr Model Discovery of particle nature of light began to break down the division that existed in 19 th -century physics between EM radiation (wave phenomenon) and small particles Atomic spectroscopy is the study of EM radiation absorbed and emitted by atoms Observations suggested wave nature of particles

33 Light and the Dilemma of Atomic Spectral Lines Experiments show that when white light is passed through a prism, a continuous spectrum results Contain all wavelengths of light When a hydrogen emission spectrum in visible region is passed through a prism, a line spectrum results Only a few wavelengths of visible light pass through

34 Seeing Atomic Spectral Lines Use your diffraction grating to observe the atomic spectra of: Hydrogen Oxygen Neon

35 Just a Thought. With a partner, answer the following questions using your knowledge from your homework: How are electrons excited in this demonstration? What happens when the electrons relax? What do the different colors in a line spectrum represent? Why are the spectra for each element unique?

36 hydrogen (H) mercury (Hg) neon (Ne)

37 Planck s Quanta and Atomic Spectra In order to produce a line spectrum, atoms electrons must somehow absorb energy and then give the energy off in the form of light at a specific wavelength What is the relationship between energy and wavelength? Can we map the electrons by using these energy relationships from the emission spectrum?

38 Neils Bohr and the Atomic Model The answer is YES! Neils Bohr was one of the first to see some connection between the wavelengths an element emits and its atomic structure Related Planck s idea of quantized energies to Rutherford s atomic model

39 Bohr and the Atomic Model Bohr discovered that as the electrons in the hydrogen atoms were getting excited and then releasing energy, only four different color bands of visible light were being emitted: red, bluish-green, and two violet-colored lines If electrons were randomly situated, as depicted in Rutherford s atomic model, then they would be able to absorb and release energy of random colors of light Bohr concluded that electrons were not randomly situated Instead, they are located in very specific locations that we now call energy levels

40 Bohr model of the Hydrogen Atom Protons and neutrons compose the nucleus Electrons orbit the nucleus in certain well-defined energy levels Niels Bohr nucleus

41 Bohr s Model of the Atom Bohr suggested that electrons typically have the lowest energy possible (ground state), but upon absorbing energy via heat or electricity: Electrons jump to a higher energy level, producing an excited and unstable state Those electrons can t stay away from the nucleus in those high energy levels forever so electrons would then fall back to a lower energy level

42 Just a Thought But if electrons are going from high-energy state to a lowenergy state, where is all this extra energy going?

43 Connecting Planck s Quanta to the Atomic Model Energy does not disappear First Law of Thermodynamics! Electrons re-emit the absorbed energy as photons of light Difference in energy would correspond with a specific wavelength line in the atomic emission spectrum Larger the transition the electron makes, the higher the energy the photon will have

44 What is the Change in Energy when Electrons Move Between Energy Levels? E = J n final n initial n = principal quantum number Energy level - E means electron emits a photon of light + E means electron absorbs a photon of light

45 More Useful Equation After some substitutions and rearranging of the previous equation, the possible wavelengths of the photons emitted by a hydrogen atom as its electron makes transitions between different energy levels are: 1 λ = R 1 n f 2 1 n i 2 R = Rydberg constant = x 10 7 m -1

46 More on Hydrogen Spectral Lines Transitions to the ground-state (n f = 1) give rise to spectral lines in the UV region of EM spectrum Set of lines is called the Lyman series Transitions to the first excited state (n f = 2) give rise to spectral lines in the visible region of EM spectrum Set of lines is called the Balmer series Transitions to the second excited state (n f = 3) give rise to spectral lines in the IR region of EM spectrum Set of lines is called the Paschen series

47 Many Electron Atoms Recall that because each element has a different electron configuration and a slightly different structure, the colors that are given off by each element are going to be different Thus, each element is going to have its own distinct color when its electrons are excited (or its own atomic spectra)

48 Shortcomings of the Bohr Model Bohr s model was too simple Worked well with only hydrogen because H only has one electron Could only approximate spectra of other elements with more than one electron Electrons do not move in circular orbits So there is more to the atomic puzzle

49 The Wave Nature of Matter de Broglie, the Uncertainty Principle, and Quantum Mechanics

50 Dual Nature of Matter?! As a result of Planck s and Einstein s work, light was found to have certain characteristics of particulate matter No longer purely wavelike But is the opposite also true? Does matter exhibit wave properties? Yes! Enter the French physicist Louis de Broglie in 1923

51 de Broglie and Wave Nature of Matter de Broglie derived an equation that relates mass, wavelength, and velocity for any object NOT traveling at the speed of light: λ = h mν This equation shows that the more massive the object, the smaller its associated wavelength and vice versa! Hence the reason why on the macroscopic level, objects do not seem to act as waves! Experimentally confirmed by two employees of Bell Laboratories (in NYC) - Davisson and Germer Beam of electrons was diffracted like light waves by the atoms of a thin sheet of nickel foil de Broglie s relation was followed quantitatively!

52 Interpretation of de Broglie s Work Electrons bound to the nucleus are similar to standing waves Standing waves do not propagate through space Standing waves are fixed at both ends Think of a guitar or violin A string is attached to both ends and vibrates to produce a musical tone Waves are standing because they are stationary the wave does not travel along the length of the string

53 Wave Nature and Particle Nature of Electrons-Complementary Properties Complementary properties mean that the more you know about one, the less you know about the other Velocity of an electron is related to its wave nature Position of an electron is related to its particle nature Particles have well-defined positions; waves do not We are unable to observe an electron simultaneously as both a particle and a wave Therefore, we cannot simultaneously measure its position AND velocity Heisenberg Uncertainty Principle

54 Heisenberg Uncertainty Principle and Complementary Properties There is a fundamental limitation on how precisely we can know both the position and momentum of a particle at a given time It is impossible to know both the velocity and location of an electron at the same time

55 How Can Something be Both a Particle and a Wave? Saying that an object is both a particle and a wave is saying that an object is both a circle and a square a contradiction Complementary solves this problem An electron is observed as either a particle or a wave, but never both at once!

56 Energies and Electrons Introducing the Quantum Mechanical Model Many properties of an element depend on the energies of its electrons Remember, position and velocity of the electron are complementary properties Since velocity is directly related to energy via ½ mv 2, position and energy are also complementary properties Therefore, we can specify the energy of the electron precisely, but not its location at a given instant Instead, the electron s position is described as a probable location where the electron is likely to be found called an orbital Enter Schrӧdinger

57 Schrödinger Equation Mathematical derivation of energies and orbitals comes from solving the Schrödinger equation: h2 d 2 Ψ 8π 2 m dx 2 + VΨ = EΨ General equation: ĤΨ = EΨ Ĥ = set of mathematical instructions called an operator that represent the total energy (kinetic and potential) of the electron within the atom Ψ = Wave function that describes the wavelike nature of the electron Orbitals Solution of the equation has demonstrated that E (energy) must occur in integer multiples Quanta!

58 Orbitals Orbitals are NOT circular orbits for electrons Orbitals ARE areas of probability for locating electrons Square of absolute value of the wave function gives a probability distribution Ψ 2 Electron density maps (probability distribution) indicates the most probable distance from the nucleus

59 Orbitals Wave functions and probability maps DO NOT describe: How an electron arrived at its location Where the electron will go next When the electron will be in a particular location

60 Quantum Numbers Each electron has a specific address in the space around a nucleus An electrons address is given as a set of four quantum numbers Each quantum number provides specific information on the electrons location

61 Electron Configuration state town house number street

62 Electron configuration (quantum numbers) state (energy level) - quantum number n town (shape of orbital) - quantum number l street (orbital room) - quantum number ml house number (electron spin) - quantum number ms

63 Principal Quantum Number (n) Same as Bohr s n Integral values: 1, 2, 3,. Indicates probable distance from the nucleus Higher numbers = greater distance from nucleus Greater distance = less tightly bound = higher energy

64 Angular Momentum Quantum Number (l) Integral values from 0 to n - 1 for each principal quantum number n Indicates the shape of the atomic orbitals Table 7.1 Angular momentum quantum numbers and corresponding atomic orbital numbers Value of l Letter used s p d f g

65 Magnetic Quantum Number (m l ) Integral values from l to -l, including zero Relates to the orientation of the orbital in space relative to the other orbitals 3-D orientation of each orbital

66 Magnetic Quantum Number

67 Electron Spin Quantum Number (m s ) An orbital can hold only two electrons, and they must have opposite spins Spin can have two values, +1/2 and -1/2 Pauli Exclusion Principle (Wolfgang Pauli) "In a given atom no two electrons can have the same set of four quantum numbers"

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69 Orbital Shapes Size of orbitals Defined as the surface that contains 90% of the total electron probability Orbitals of the same shape (s, for instance) grow larger as principal quantum number (n) increases # of nodes (areas in which there is zero electron probability) increase as well

70 Why Do We Care About the Shape of the Orbitals? Covalent chemical bonds depend on the sharing of the electrons that occupy these orbitals Shape of overlapping orbitals determine the shape of the molecule!

71 s sub-level (l = 0) spherical shape single orbital seen in all energy levels

72 p sub-level (l = 1) y-axis p (x) z-axis p (y) x-axis p (z)

73 d sub-level (l = 2) five clover-shaped orbitals seen in all energy levels n=3 and above

74 f sub-level (l = 3) seven equal energy orbitals shape is not well-defined seen in all energy levels n=4 and above

75 Orbital Energies Electron in lowest energy state Ground state When an atom absorbs energy, electrons may move to higher orbitals Excited state

76 Orbital Energies in Polyelectronic Atoms Polyelectronic atoms are atoms with more than one electron Atoms other than hydrogen Must make approximations with quantum mechanical model to compensate for repulsions between electrons Variations in energy within the same quantum level Atoms other than hydrogen have variations in energy for orbitals having the same principal quantum number Electrons fill orbitals of the same n value in preferential order E n-s < E n-p < E n-d < E n-f Electron density profiles show that s electrons penetrate to the nucleus more than other orbital types Closer proximity to the nucleus = lower energy

77 Orbital Energies

78 Using the Periodic Table to Predict Electron Locations Aufbau principle Electrons are added one at a time to the lowest energy orbitals available until all the electrons of the atom have been accounted for aufbau German for build up or construct

79 Hund s Rule Electrons must fill a sub-level such that each orbital has a spin up electron before they are paired with spin down electrons

80 Orbital Diagrams and Electron Configurations Electrons fill in order from lowest to highest energy The Pauli exclusion principle holds. An orbital can hold only two electrons Two electrons in the same orbital must have opposite signs You must know how many electrons can be held by each orbital 2 for s 6 for p 10 for d 14 for f Hund s rule applies. The lowest energy configuration for an atom is the one having the maximum number of unpaired electrons for a set of degenerate orbitals By convention, all unpaired electrons are represented as having parallel spins with the spin up

81 aufbau chart 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f