Quantum Mechanical Model of the Atom PDF

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Quantum Mechanical Model of the Atom ____________________________________________________________ Light as a wave ●

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Electromagnetic radiation ○ Form of energy that has wave characteristics and is propagated through space at the speed of light ■ 3.00 x 10 to 8 m/s ○ Electrical and magnetic characteristics ○ Wave is composed oscillating electric and magnetic fields Wavelength ○ Distance from peak to peak Amplitude ○ Vertical height of the peak of the wave ○ Related to brightness/intensity Frequency ○ Number of cycles for wave peaks that pass a given point per unit of time, usually seconds

Relationship between frequency and wavelength ● ●

c= wavelength( frequency) Red light from a laser pointer has a wavelength of 650 nm. What is its frequency ○ 3.00 x 10 to 8 m/s = 650 nm x frequency ○ freq= 3.00 x 10 to 8 m/s/ 650nm ○ 4.76 x 10 to 14 s to -1

Photoelectric effect ● ●

Metal surface emit e- when irradiated with EM above a certain wavelength Light energy transferred to e-

Einstein ●

Light energy is composed of tiny packets of energy called “QUANTA” alpha “PHOTONS”

Max Planck ● ● ● ●

Energy can be absorbed or emitted in discrete bundle called “Quanta” Each frequency has a different energy associated with it E photon= hv= hc/ λ What is the energy of a photon of light with wavelength of 450nm

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6.62 x10 -34 j-s x 3.00 x 10 8 m s-1 / 450 nm ■ 4.42 x 10 -19 J What is the energy in joule per mole ■ 4.42 x 10 -19 J X 6.022 x 10 23 ● 266000 j/mol

Bohr ● ● ● ●

Electrons in an atom can only live at certain discrete energies Atom absorbs or emits EMR when electron moves from one energy level to another An atom emits light when the electron moves from a higher level to a lower level An atom absorbs light when the electron travels from a higher level to s lower level

Schroedinger ●

Wave equation ○ Φ ■ Wave equation ■ Solution based on three numbers 2 ○ Ψ ■ Probability of finding an electron at some point in space

Probability distribution ● ● ●

Can’t know exactly where electron is located Define areas in space with high probability of finding electrons Orbital ○ Probability distribution map ○ Shows volume in which an electron can be found ○ Important to bonding ○ Defined by 3 quantum numbers (interrelated) ■ Principle quantum number, n ● Integer ● Defines size and energy of an orbital ● An n increases probability of finding electron moves farther from nucleus and energy of orbital increases ○ Spacing decreases ○ Electrons are more easily removed ■ Angular momentum, l ● Defines shape of orbital ● Allowed values depend on “n” ○ 0 to n -1 ○ Expressed as orbital notation ■

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l

Orbital notation

#orbitals

Shape

0

s

1

sphere

1

p

3

dumbell

2

d

5

3

f

7

4

g

9

5

h

11

Magnetic quantum number, m l ● Depends on l ● Defines orbital orientation in space ● Allowed values ○ 0, +/- 1, +/- 2, … +/- l

Shell ■ Is a collection of orbitals with same values of n Sub shell ■ Is a collection of orbitals with same values of n and l Orbital ■ Defined by n, l and ml ■ Can hold at most 2 electrons of opposite spin Spin quantum number, ms ■ Not mathematical ● + ½, - ½

○ n

l

ml

Orbital #

Count of orbitals

1

0

0,

1,0,0

1

2

0 1

-1 0 +1

2,00 2,1,-1 2,1,0 2,1,1

4

3

0 1 2

-2 -1 0

3,0,0 3,1,-1

9

+1 +2

3,1,0 3,1,1 3,2,0 3,2,-1

3,2,-2 3,2,1 3,2,2

○ Paired electrons ●

2 electrons in one orbital each having opposite spin

Change in energy ●

Change in energy= 2. 18 x 10 -18 J (1/ n 2 f - 1/n2 t) ‘’ ○ 2. 18 x 10 -18 J (1/ n22 f - 1/42 t) ■ -4.09 x 10 -19 J ○ What is the wavelength of em emitted ■ E= hc/ λ ■ λ= hc/E ■ 6.626 x10 -34 x 3.00 x10 8 m.s/-4.09 x 10 -19 J ● 4.86 x 10 -7 m ● 486 nm

Degenerate ●

Orbitals that have same energia

Orbital stability ●

Half filled and filed degenerate orbitals are more stable than expected ○ Most important for d and f elements as well as some p element properties

Definitions ●

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Valence electrons (outer shell electrons) ○ Electrons in the outermost energy level ○ Have highest value of n in an electron configuration ○ Important in bonding of elements Core electrons (inner shell electrons) ○ Electrons in completed subshells ■ D and f orbitals ○ Not involved in bonding of elements

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○ Do not have highest value of n Inner shell configuration ○ Use short in which the the symbol for the preceding noble gas is use to represent part of the electromagnetic configuration Noble gas configurations ○ Exceptionally stable ○ Cations tend to lose electrons till there configuration is ns2np2 ■ Not transitional ○ Anions tend to gain electrons till there configuration is ns2np2 ■ Not transitional ○ Electron configuration ■ Anions ● Determine number of electrons ● Determine ground state ■ Cations ● Draw electronic configuration of element ● Remove electrons ○ From highest value of n first ○ Atomic radius ■ Is ½ the distance between the nuclei to bonded atoms ○ Z effective nuclear charge ■ Z-s ● S- shielding electrons ○ Number of electrons between electron and nucleus ○ Have smaller n ○...