Chapter 7Wave Formulas

Energy of one photon

E=hν=hcλ E = energy (Joules)

h = Planck’s constant = 6.626 x 10-34 J·sν = frequency (s-1 = 1/s = Hz)c = speed of light (and all electromagnetic radiation) = 3 x 108 m/sλ = wavelength (meters)

Equation is for one photon which is absorbed by or released from one atom.Often you are asked about 1 mole of atoms, use Avogadro’s number 6.022 x 1023 atoms/mole

Shortcut: nm = x 10-9 m 580 nm = 580 x 10-9 m1 kJ = 1000 J

Visible light 400-700 nm 400 is violet high energy, 700 is red low energyHigher energy = higher frequency = smaller wavelengthLower energy = lower frequency = larger wavelength

DeBroglie wave-particle duality equation (for an object with mass, not pure energy)

λ= hmv λ = wavelength (meters)

h = Planck’s constant = 6.626 x 10-34 J·sm = mass of object (kg)v = speed of object (m/s)

A large object has very small wavelength, so we don’t “see” the wave nature of large objects.

Mass of an electron me = 9.11 x 10-31 kgMass of a proton mp = 1.67 x 10-27 kg

Rydberg equation for Hydrogen atomλ = wavelength (meters)

RH constant = 1.0973731 x 107 m-1

nf = final level, ending level ni = initial level, starting level

Energy to change levels in Hydrogen atom

△E=hcλ =hc 1λ=hc ∙RH ( 1nf2−

1ni2 )

△E=−2.178 x10−18 J ( 1n f2−1ni2 )

△E= energy (Joules)nf = final level, ending levelni = initial level, starting level

when e- moves from higher level to lower level, energy is released, negative △Ewhen e- moves from lower level to higher level, energy is absorbed, positive △E

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Chapter 7Energy to remove an electron from a certain level of Hydrogen atom

△E=−2.178 x10−18 J ( 1∞2− 1ni2 ) △E=−2.178 x10−18 J (0− 1ni2 ) = △E=2.178 x10−18 J ( 1ni2 )

△E= energy (Joules)nf = final level, ending levelni = initial level, starting level

Energy level of a Hydrogen atom

En = -2.178 x 10-18 J (Z2n2 ) E = energy (Joules)

Z = nuclear chargen = energy level

Energy when electron is very far away = 0

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Chapter 7

Electron configuration

1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 7s2 5f14 6d10 7p6

Orbitals have different shapes s p d fTwo electrons fit into each orbital. The two electrons will have opposite spins.

d

pz px py

f

**g h i orbitals not used in ground state of any element on the periodic table. only s p d f.

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Chapter 7Electron configuration

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Chapter 7

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Chapter 7Orbital diagram

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Chapter 7

a. Atom radius increases to the Left in same row, increases going down a column ↓i. As move to right, more protons, same distance to electrons in same shell, more pull toward

center, atom size decreases to Right in same row.As move down a column, increased number of shells means larger atom. Periodic Trends

1. Atomic Radiusa. Radius of atom shows size of atom. Larger radius = larger atomb. Radius is from nucleus to valence electron in outermost shell.c. Coulomb’s Law, electrostatic force between two charges

i. F = k q1q2r2

F = force k = constant q1 and q2 are charges r = distance between chargesii. Higher charge is more force

iii. Larger distance is less forced. Nucleus pulls all electrons toward center. (pos and neg attract), more protons = more forcee. Electrons repel each other (both negative)f. Shielding electrons in inner shells (not valance shell) reduce the strength of the pull from the nucleus

toward valence shell e-.g. Zeff = effective nuclear charge. Zeff = # protons – # shielding e-

i.h. Cation size < atom size (Na+ < Na) with loss of valance e-‘s, drop down to smaller shelli. Anion size > atom size (F- > F) more e- repulsions, same protons.j. General rules:

i. If same # protons, more e- is larger atom/ionii. If same # e-, more protons is smaller atom/ion

k. “isoelectronic” means same # electrons, same electronic configuration, higher protons = smaller ion/atom Mg2+ < Na+ < Ne < F- < O2-

In this diagram,

Shielding electrons are in shell 1 and 2 Valence electrons are in shell 3

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Electrostatic attraction = positive nucleus and negative electron. Nucleus pulls electrons inward.

Electrostatic repulsion = negative electron and negative electron. Electrons push apart from each other.

Chapter 72. Ionization Energy

a. Ionization energy = energy needed to pull an electron away from a gaseous atom in ground state, to create an ion. Usually expressed in kJ/mol, or the amount of energy it takes for all the atoms in a mole to lose one electron each.

b. Always endothermic, always must add energy to remove electron. e - is attracted to nucleus.c. First ionization energy I1 = energy to remove the first e- from an atom.d. Second ionization energy I2 = energy to remove the second e- from an atom. Always higher energy than

I1 e. The more tightly held the e- , the more energy needed to remove it. f. Ionization Energy “generally” increases to right in the same row, increases going up a column.

i. As move to right, more protons, same distance to electrons in same shell, more pull toward center, higher ionization energy

ii. As move down a column, increased number of shells means larger atom, less pull on outer electrons, lower ionization energy

iii. Exceptions: As go across a row to the right, I 1 increases except element after a full orbitals (boron) or after a half full orbitals (oxygen) situation.

g. Ionization energy is much, much higher when removing the first e- from a full octet.Al Al+ I 1 = 580 kJ/molAl+ Al2+ I2 = 1815 kJ/molAl2+ Al3+ I 3 = 2740 kJ/molAl3+ Al4+ I 4 = 11600 kJ/mol

3. Electron Affinitya. Electron affinity = energy change to add an electron to a gaseous atom.b. A negative electron affinity = energy is released when an atom is added, exothermicc. The more negative the energy, the greater amount of energy released.d. EA is more negative as move to Right in a row and up a column ↑

i. As move to right in same row, more protons, same distance to electrons in same shell, more pull toward center, atom pulls in e- more strongly, more energy benefit, more energy released.

ii. As move down a column, increased number of shells means e- not attracted as strongly, less energy benefit, less energy released.

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