• Electromagnetic Radiation • Light is an electromagnetic wave, that
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Electromagnetic Radiation Light is an electromagnetic wave, that travels with a constant speed of: c = 𝝀𝝂 = 𝟑. 𝟎𝟎 × 𝟏𝟎𝟖 𝒎/𝒔 = frequency (s-1) = wavelength (m) Light is a particle, or a photon, and the energy of a photon of light is equal to: 𝒉𝒄 𝑬 = 𝒉𝝂 = 𝝀 h = Planck’s constant (6.626 x 10-34 J s) Photoelectric effect: light strikes the surface of a metal, electrons are ejected Work function: minimum quantity of energy needed to extract an electron from a metal’s surface. 𝜱 = 𝒉𝝊𝒐 o = threshold frequency (s-1) = work function The remainder of the energy from the photon is transferred to the electron in the form of kinetic energy 𝑬𝑲 = 𝑬𝒑𝒉𝒐𝒕𝒐𝒏 − 𝜱 𝑬𝑲 = 𝒉𝝊 − 𝒉𝝊𝒐 de Broglie proposed that all matter experiences wave-particle duality 𝒉 𝒉 𝝀= = 𝒑 𝒎𝒗 v = velocity (m/s) p = momentum (kg m s-1) m = mass The emission spectrum of an element is made by heating up the element until it glows and then sending the light through a prism. Each element has an emission spectrum unique to that element. The absorption spectrum is made by sending light through the gaseous state of the element and then refracting the remaining light through a prism. Bohr’s model of the atom: atoms have definite and discrete number of energy levels (orbits) For one-electron species, energy of a particular n level is: 𝑹𝑯 𝑬𝒏 = − 𝟐 𝒏 RH = Rydberg’s constant (2.18 x 1018 J) The energy of an allowed transition is then equal to: 𝟏 𝟏 ∆𝑬 = −𝑹𝑯 × ( 𝟐 − 𝟐 ) 𝒏𝒇 𝒏𝒊 The energy of a photon from an allowed transition (either absorbed or emitted): 𝑬𝒑𝒉𝒐𝒕𝒐𝒏 = 𝒉𝝊 = |∆𝑬|
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We can calculate the energy levels hydrogen-like species, such as Li2+ or Be3+ 𝒁𝟐 𝑬𝒏 = −𝑹𝑯 𝟐 (only works for species with 1 electron!) 𝒏 Z = atomic number Quantum Number
Values
Interpretation
n (principal quantum number)
1, 2, 3, …
“size” All orbitals with the same principle quantum number have the same magnitude of energy and are said to be in the same shell
𝓁 (orbital angular momentum quantum bumber)
0, 1, 2, …, n-1
“shape” Shells are divided into subshells which identifies the different shapes (0=s, 1=p, 2=d, 3=f) for orbitals.
m𝓁 (magnetic quantum number)
-𝓁, …, 0, …, 𝓁
“orientation” Subshells are divided into the individual orbitals
ms (magnetic spin quantum number)
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1
1
2
2
+ ;−
“spin” An electron behaves like a magnet that has one of two possible orientations, aligned either with the magnetic field or against it.
Quantum numbers describing an orbital: n, 𝓁, m𝓁 Quantum numbers describing an electron: n, 𝓁, m𝓁, ms
z
s-orbitals
x
y
px
py
pz y
y
y
p-orbitals x
z
d-orbitals
x
z
x
z
dxz
dxy
dyz
z
y
z
x
x
dx2 -y2
dz 2 z
y y
x Y
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x
Pauli’s Exclusion Principle: No two electrons in an atom can have the same values of all four quantum numbers (n, l, ml, ms). Each orbital can hold up to 2 electrons each s orbitals: 2 electrons p orbitals: 2 x 3 = 6 electrons d orbitals: 2 x 5 = 10 electrons Aufbau Principle: electrons will always occupy the lowest available energy level first
Hund’s Rule: electrons do not pair up until all the orbitals of an energy level are filled with one electron
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Electromagnetic Radiation Light is an electromagnetic wave, that travels with a constant speed of: c = 𝝀𝝂 = 𝟑. 𝟎𝟎 × 𝟏𝟎𝟖 𝒎/𝒔 = frequency (s-1) = wavelength (m) Light is a particle, or a photon, and the energy of a photon of light is equal to: 𝒉𝒄 𝑬 = 𝒉𝝂 = 𝝀 h = Planck’s constant (6.626 x 10-34 J s) Photoelectric effect: light strikes the surface of a metal, electrons are ejected Work function: minimum quantity of energy needed to extract an electron from a metal’s surface. 𝜱 = 𝒉𝝊𝒐 o = threshold frequency (s-1) = work function The remainder of the energy from the photon is transferred to the electron in the form of kinetic energy 𝑬𝑲 = 𝑬𝒑𝒉𝒐𝒕𝒐𝒏 − 𝜱 𝑬𝑲 = 𝒉𝝊 − 𝒉𝝊𝒐 de Broglie proposed that all matter experiences wave-particle duality 𝒉 𝒉 𝝀= = 𝒑 𝒎𝒗 v = velocity (m/s) p = momentum (kg m s-1) m = mass The emission spectrum of an element is made by heating up the element until it glows and then sending the light through a prism. Each element has an emission spectrum unique to that element. The absorption spectrum is made by sending light through the gaseous state of the element and then refracting the remaining light through a prism. Bohr’s model of the atom: atoms have definite and discrete number of energy levels (orbits) For one-electron species, energy of a particular n level is: 𝑹𝑯 𝑬𝒏 = − 𝟐 𝒏 RH = Rydberg’s constant (2.18 x 1018 J) The energy of an allowed transition is then equal to: 𝟏 𝟏 ∆𝑬 = −𝑹𝑯 × ( 𝟐 − 𝟐 ) 𝒏𝒇 𝒏𝒊 The energy of a photon from an allowed transition (either absorbed or emitted): 𝑬𝒑𝒉𝒐𝒕𝒐𝒏 = 𝒉𝝊 = |∆𝑬|
•
We can calculate the energy levels hydrogen-like species, such as Li2+ or Be3+ 𝒁𝟐 𝑬𝒏 = −𝑹𝑯 𝟐 (only works for species with 1 electron!) 𝒏 Z = atomic number Quantum Number
Values
Interpretation
n (principal quantum number)
1, 2, 3, …
“size” All orbitals with the same principle quantum number have the same magnitude of energy and are said to be in the same shell
𝓁 (orbital angular momentum quantum bumber)
0, 1, 2, …, n-1
“shape” Shells are divided into subshells which identifies the different shapes (0=s, 1=p, 2=d, 3=f) for orbitals.
m𝓁 (magnetic quantum number)
-𝓁, …, 0, …, 𝓁
“orientation” Subshells are divided into the individual orbitals
ms (magnetic spin quantum number)
• •
1
1
2
2
+ ;−
“spin” An electron behaves like a magnet that has one of two possible orientations, aligned either with the magnetic field or against it.
Quantum numbers describing an orbital: n, 𝓁, m𝓁 Quantum numbers describing an electron: n, 𝓁, m𝓁, ms
z
s-orbitals
x
y
px
py
pz y
y
y
p-orbitals x
z
d-orbitals
x
z
x
z
dxz
dxy
dyz
z
y
z
x
x
dx2 -y2
dz 2 z
y y
x Y
•
•
•
x
Pauli’s Exclusion Principle: No two electrons in an atom can have the same values of all four quantum numbers (n, l, ml, ms). Each orbital can hold up to 2 electrons each s orbitals: 2 electrons p orbitals: 2 x 3 = 6 electrons d orbitals: 2 x 5 = 10 electrons Aufbau Principle: electrons will always occupy the lowest available energy level first
Hund’s Rule: electrons do not pair up until all the orbitals of an energy level are filled with one electron
