Chapter 4a_electronic Atomic Structure

CHAPTER 4

Electronic Structure of Atom From Indivisible to Quantum Mechanical Model of the Atom

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Classical Model Democritus Dalton Thomson Rutherford

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Democritus Circa 400 BC Greek philosopher Suggested that all matter is composed of tiny, indivisible particles, called atoms

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Dalton’s Atomic Theory (1808) 1. All matter is made of tiny indivisible particles called 2. 3. 4.

atoms. Atoms of the same element are identical. The atoms of any one element are different from those of any other element. Atoms of different elements can combine with one another in simple whole number ratios to form compounds. Chemical reactions occur when atoms are separated, joined, or rearranged; however, atoms of one element are not changed into atoms of another by a chemical reaction.

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J.J. Thomson (1897) Determined the charge to mass ratio for electrons Applied electric and magnetic fields to cathode rays (waves) “Plum pudding” model of the atom

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Rutherford’s Gold Foil Experiment (1910) Alpha particles (positively charged helium ions) from a radioactive source was directed toward a very thin gold foil. A fluorescent screen was placed behind the Au foil to detect the scattering of alpha (α ) particles.

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Rutherford’s Gold Foil Experiment (Observations) Most of the α -particles passed through the foil. Many of the α -particles deflected at various angles. Surprisingly, a few particles were deflected back from the Au foil.

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Rutherford’s Gold Foil Experiment (Conclusions) Rutherford concluded that most of the mass of an atom is concentrated in a core, called the atomic nucleus. The nucleus is positively charged. Most of the volume of the atom is empty space.

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Shortfalls of Rutherford’s Model Did not explain where the atom’s negatively charged electrons are located in the space surrounding its positively charged nucleus. We know oppositely charged particles attract each other What prevents the negative electrons from being drawn into the positive nucleus? 10

Bohr Model (1913) Niels Bohr (1885-1962), Danish scientist working with Rutherford Proposed that electrons must have enough energy to keep them in constant motion around the nucleus Analogous to the motion of the planets orbiting the sun 11

Planetary Model The planets are attracted to the sun by gravitational force, they move with enough energy to remain in stable orbits around the sun. Electrons have energy of motion that enables them to overcome the attraction for the positive nucleus 12

Think about satellites…. We launch a satellite into space with enough energy to orbit the earth The amount of energy it is given, determines how high it will orbit We use energy from a rocket to boost our satellite. 13

Electronic Structure of Atom Waves-particle duality Photoelectric effect Planck’s constant Bohr model de Broglie equation

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Radiant Energy Radiation ≡ the emission of energy in various forms A.K.A. Electromagnetic Radiation Radiant Energy travels in the form of waves that have both electrical and magnetic impulses Electromagnetic Radiation ≡ radiation that consists of wave-like electric and magnetic fields in space, including light, microwaves, radio signals, and xrays Electromagnetic waves can travel through empty space, at the speed of light (c=3.00x108m/s) or about 300million m/s!!!

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Waves 

Waves transfer energy from one place to another •

•



Think about the damage done by waves during strong hurricanes. Think about placing a tennis ball in your bath tub, if you create waves at one it, that energy is transferred to the ball at the other = bobbing

Electromagnetic waves have the same characteristics as other waves

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Wave Characteristics

Wavelength, λ (lambda) ≡ distance between successive points 2 m

10 m

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Wave Characteristics Frequency, ν (nu) ≡ the number of complete wave cycles to pass a given point per unit of time; Cycles per second

t=0

t=5

t=0

t=5

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Units for Frequency 1 cycle/s s-1 hertz, Hz Because all electromagnetic waves travel at the speed of light, wavelength is determined by frequency Low frequency = long wavelengths High frequency = short wavelengths

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Waves Amplitude ≡ maximum height of a wave

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Waves Node ≡ points of zero amplitude

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Electromagnetic Spectrum Radio & TV, microwaves, UV, infrared, visible light = all are examples of electromagnetic radiation (and radiant energy) Electromagnetic spectrum: entire range of electromagnetic radiation

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Electromagnetic Spectrum 1024

1020

Gamma

10-16

10-9

1018 1016 1014

Xrays

10-8

UV

1012

IR

10-6

1010

Frequenc y Hz 108 106

Microwaves FM AM

10-3

100

102Wavelength m

Visible Light

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Notes Higher-frequency electromagnetic waves have higher energy than lower-frequency electromagnetic waves All forms of electromagnetic energy interact with matter, and the ability of these different waves to penetrate matter is a measure of the energy of the waves

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What is your favorite radio station? Radio stations are identified by their frequency in MHz. We know all electromagnetic radiation(which includes radio waves) travel at the speed of light. What is the wavelength of your favorite station? 25

Velocity of a Wave Velocity of a wave (m/s) = wavelength (m) x frequency (1/s) c=λ ν c= speed of light = 3.00x108 m/s Eg: My favorite radio station is 105.9 Jamming Oldies!!! What is the wavelength of this FM station?

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Wavelength of FM Answer:

c =λ ν c= speed of light = 3.00x108 m/s ν = 105.9MHz or 1.059x108Hz λ = c/ν = 3.00x108 m/s = 2.83m 1.059x1081/s

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What does the electromagnetic spectrum have to do with electrons? It’s all related to energy - energy of motion (of electrons) and energy of light

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Light

States of Electrons When current is passed through a gas at a low pressure, the potential energy (energy due to position) of some of the gas atoms increases. Ground State: the lowest energy state of an atom Excited State: a state in which the atom has a higher potential energy than it had in its ground state 30

Excited State

Absorbance and Emission

Absorbance and Emission

Quantization

Neon Signs When an excited atom returns to its ground state it gives off the energy it gained in the form of electromagnetic radiation! The glow of neon signs, is an example of this process

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White Light White light is composed of all of the colors of the spectrum = ROY G BIV When white light is passed through a prism, the light is separated into a spectrum, of all the colors What are rainbows?

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Line-emission Spectrum When an electric current is passed through a vacuum tube containing H2 gas at low pressure, and emission of a pinkish glow is observed. What do you think happens when that pink glow is passed through a prism? 37

Hydrogen’s Emission Spectrum The pink light consisted of just a few specific frequencies, not the whole range of colors as with white light Scientists had expected to see a continuous range of frequencies of electromagnetic radiation, because the hydrogen atoms were excited by whatever amount of energy was added to them. Lead to a new theory of the atom

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Bohr’s Model of Hydrogen Atom Hydrogen did not produce a continuous spectrum New model was needed: 





Electrons can circle the nucleus only in allowed paths or orbits When an e- is in one of these orbits, the atom has a fixed, definite energy e- and hydrogen atom are in its lowest energy state when it is in the orbit closest to the nucleus 39

Bohr Model Continued…  

Orbits are separated by empty space, where e- cannot exist Energy of e- increases as it moves to orbits farther and farther from the nucleus

(Similar to a person climbing a ladder)

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Bohr Model and Hydrogen Spectrum While in orbit, e- can neither gain or lose energy But, e- can gain energy equal to the difference between higher and lower orbitals, and therefore move to the higher orbital (Absorption) When e- falls from higher state to lower state, energy is emitted (Emission)

Bohr’s Calculations Based on the wavelengths of hydrogen’s lineemission spectrum, Bohr calculated the energies that an e- would have in the allowed energy levels for the hydrogen atom 41

Photoelectric Effect An observed phenomenon, early 1900s When light was shone on a metal, electrons were emitted from that metal Light was known to be a form of energy, capable of knocking loose an electron from a metal Therefore, light of any frequency could supply enough energy to eject an electron.

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Photoelectric Effect : Situation Light strikes the surface of a metal (cathode), and e- are ejected. These ejected e- move from the cathode to the anode, and current flows in the cell. A minimum frequency of light is used. If the frequency is above the minimum and the intensity of the light is increased, more e- are ejected.

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Photoelectric Effect cont. Observed: For a given metal, no electrons were emitted if the light’s frequency was below a certain minimum, no matter how long the light was shone Why does the light have to be of a minimum frequency?

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Explanation…. Max Planck studied the emission of light by hot objects Proposed: objects emit energy in small, specific amounts = quanta (Differs from wave theory which would say objects emit electromagnetic radiation continuously)

Quantum: is the minimum quantity of energy that can be lost or gained by an atom.

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Planck’s Equation E radiation = Planck’s constant x frequency of radiation E = hν h = Planck’s constant = 6.626 x 10-34 J s •

When an object emits radiation, there must be a minimum quantity of energy that can be emitted at any given time.

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Einstein Expands Planck’s Theory Theorized that electromagnetic radiation had a dual wave-particle nature! Behaves like waves and particles Think of light as particles that each carry one quantum of energy = Photons photons

Photons: a particle of electromagnetic radiation having zero mass and carrying a quantum of energy Ephoton = hν 47

Back to Photoelectric Effect Einstein concluded: 



Electromagnetic radiation is absorbed by matter only in whole numbers of photons In order for an e- to be ejected, the e- must be struck by a single photon with minimum frequency

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Example of Planck’s Equation CD players use lasers that emit red light with a λ of 685 nm. Calculate the energy of one photon. 

Different metals require different minimum frequencies to exhibit photoelectric effect

Answer Ephoton

= hν

h = Planck’s constant = 6.626 x 10-34 J•s c =λ ν c = speed of light = 3.00x108 m/s ν = (3.00x108 m/s)/(6.85x10-7 m) ν = 4.37x1014 1/s Ephoton = (6.626 x 10-34 J•s)(4.37x1014 1/s) Ephoton = 2.90 x 10-19 J

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Wave Nature of Electrons We know electrons behave as particles In 1925, Louis de Broglie suggested that electrons might also display wave properties

de Broglie’s Equation A free e- of mass (m) moving with a velocity (v) should have an associated wavelength: λ = h/mv Linked particle properties (m and v) with a wave property (λ ) 50

Example of de Broglie’s Equation Calculate the wavelength associated with an e- of mass 9.109x10-28 g traveling at 40.0% the speed of light. [Hint.: 1 J = 1 kg m2/s2] Answer: v=(3.00x108m/s)(.40)=1.2x108m/s

λ = h/mv λ = (6.626 x 10

-34

J•s)

=6.06x10-12 m

(9.11x10-31 kg)(1.2x108m/s) Remember 1J = 1(kg)(m)2/s2

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Wave-Particle Duality de Broglie’s experiments suggested that e- has wave-like properties. Thomson’s experiments suggested that e- has particle-like properties 

measured charge-to-mass ratio

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Quantum mechanical model SchrÖdinger Heisenberg Pauli Hund

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Where are the e- in the atom? e- have a dual wave-particle nature If e- act like waves and particles at the same time, where are they in the atom? First consider a theory by German theoretical physicist, Werner Heisenberg.

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Heisenberg’s Idea e- are detected by their interactions with photons Photons have about the same energy as eAny attempt to locate a specific e- with a photon knocks the e- off its course ALWAYS a basic uncertainty in trying to locate an e-

Heisenberg’s Uncertainty Principle Impossible to determine both the position and the momentum of an e- in an atom simultaneously with great certainty. 55

SchrÖdinger’s Wave Equation An equation that treated electrons in atoms as waves Only waves of specific energies, and therefore frequencies, provided solutions to the equation SchrÖdinger’s Wave Quantization of e- energies was a natural outcome Equation Solutions are known as wave functions Wave functions give ONLY the probability of finding and e- at a given place around the nucleus e- not in neat orbits, but exist in regions 56 called orbitals

SchrÖdinger’s Wave Equation Here is the equation Don’t memorize this or write it down It is a differential equation, and we need calculus to solve it -h = (ә2 Ψ )+ (ә2Ψ )+( ә2Ψ ) +Vψ =Eψ 8(π)2m (әx2) (әy2) (әz2 ) Scary???

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Definitions Probability ≡ likelihood Orbital ≡ wave function; region in space where the probability of finding an electron is high SchrÖdinger’s Wave Equation states that orbitals have quantized energies But there are other characteristics to describe orbitals besides energy

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Quantum Numbers Definition: specify the properties of atomic orbitals and the properties of electrons in orbitals There are four quantum numbers The first three are results from SchrÖdinger’s Wave Equation

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Quantum Numbers (1) Principal Quantum Number, n

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Quantum Numbers Principal Quantum Number, n   

Values of n = 1,2,3,… ∞ Positive integers only! Indicates the main energy level occupied by the electron

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Quantum Numbers Principal Quantum Number, n  

Values of n = 1,2,3,… ∞ Describes the energy level, orbital size

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Quantum Numbers Principal Quantum Number, n  



Values of n = 1,2,3,… ∞ Describes the energy level, orbital size As n increases, orbital size increases.

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Principle Quantum Number n=6 n=5 n=4 n=3

Energy

n=2

n=1

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Principal Quantum Number

Principle Quantum Number More than one e- can have the same n value These e- are said to be in the same eshell The total number of orbitals that exist in a given shell = n2

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Quantum Numbers (2) Angular momentum quantum number, l

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Quantum Numbers Angular momentum quantum number, l  Values of l = n-1, 0

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Quantum Numbers Angular momentum quantum number, l  Values of l = n-1, 0  Describes the orbital shape

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Quantum Numbers Angular momentum quantum number, l  Values of l = n-1, 0  Describes the orbital shape  Indicates the number of sublevel (subshells) (except for the 1st main energy level, orbitals of

different shapes are known as sublevels or subshells)

* Shape of the “volume” of space that the e- occupies 70

Orbital Shapes For a specific main energy level, the number of orbital shapes possible is equal to n. Values of l = n-1, 0  Eg. Orbital which n=2, can have one of two shapes

corresponding to l = 0 or l=1

Depending on its value of l, an orbital is assigned a letter.

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Orbital Shapes Angular magnetic quantum number, l If l = 0, then the orbital is labeled s. s is spherical. If l = 1, then the orbital is labeled p. p is “dumbbell” shape If l = 2, the orbital is labeled d. “double dumbbell” or four-leaf clover If l = 3, then the orbital is labeled f.

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Orbital Shapes

Energy Level and Orbitals n=1, only s orbitals n=2, s and p orbitals n=3, s, p, and d orbitals n=4, s,p,d and f orbitals Remember: l = n-1 Value of l

0

1

2

3

Type of orbital

s

p

d

f 74

Energy Level Transitions

Atomic Orbitals Atomic Orbitals are designated by the principal quantum number followed by letter of their subshell  

Eg. 1s = s orbital in 1st main energy level Eg. 4d = d sublevel in 4th main energy level

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Quantum Numbers (3) Magnetic Quantum Number, ml

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Quantum Numbers Magnetic Quantum Number, ml 

Values of ml = +l…0…-l

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Quantum Numbers Magnetic Quantum Number, ml  

Values of ml = +l…0…-l Describes the orientation of the orbital  Atomic orbitals can have the same

shape but different orientations * orientation of the orbital in space 79

Magnetic Quantum Number s orbitals are spherical, only one orientation, so m=0 p orbitals, 3-D orientation, so m= -1, 0 or 1 (x, y, z) d orbitals, 5 orientations, m= -2,-1, 0, 1 or 2

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Magnetic Quantum Number, ml

Quantum Numbers (4) Electron Spin Quantum Number,ms

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Quantum Numbers Electron Spin Quantum Number,ms   

Values of ms = +1/2 or –1/2 e- spin in only 1 or 2 directions A single orbital can hold a maximum of 2 e-, which must have opposite spins

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Orbital Shapes 1) s orbitals(l = 0 )

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Orbital Shapes 2) p orbitals(l = 1 )

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Orbital Shapes 3) d orbitals(l = 2 )

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orientation of the orbital in space, ml

ml = -1

ml = -2

ml = 0

ml = -1

ml = 0

ml = 1

ml = 1

ml = 2

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Spin quantum number ms ms = +½ or -½

ms = +½ ms = -½

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