Electrons, Energy, & the Electromagnetic Spectrum

Simplified, 2-D Bohr Model:

Orbits, paths, shells, rings = ENERGY LEVELS

As the name “energy level” implies, there is a
specific amount of energy associated with each
energy level.

Electrons are lazy – they will occupy the
location that requires the least amount of
energy

Lowest energy state = GROUND STATE

For hydrogen in the ground state…

~ Electron is located in energy level 1 (E 1) because E1 is closest to the
nucleus. Nucleus is positively-charged & attracts negatively-charged e-. Therefore, low amount of energy Nucleus needed to be in E1.

Electron

If energy (from an outside source) is added to the atom…

Electron jumps to a higher energy level because
energy is absorbed. (Electron is now in the
EXCITED STATE.)

As soon as the electron jumps to a higher level,
Add energy it immediately falls back to a lower energy level.
When the electron falls, energy is released.

energy The energy is released in the form of
released electromagnetic (EM) radiation.

The type or form of EM radiation released
depends on the difference in energy between
the energy levels.

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Here’s how the type/form of EM radiation can be determined…

The amount of energy released when an electron falls from a higher to a lower energy level is directly proportional to its frequency. The calculation follows the equation: E = h ^. ν

E = Energy (unit is J)
h = Planck’s Constant (6.626 x 10^-34 J^.s)
ν = frequency (unit is Hz or ¹/_second)

EXAMPLE 1: A particle of EM radiation has an energy of 1.15 x 10^-16 J. What is its frequency?
1.15 x 10^-16 J = 6.626 x 10^-34 J^.s ^. ν
ν = 1.74 x 10¹⁷ Hz

The type of electromagnetic radiation can be determined if one knows the wavelength. The wavelength is inversely proportional to the frequency. The calculation follows the equation: c = λ ^. ν

c = speed of light (3.00 x 10⁸ m/s)
λ = wavelength (unit is m)
ν = frequency (unit is Hz or ¹/_s)

EXAMPLE 2: What is the wavelength of the same particle from EXAMPLE 1?
3.00 x 10⁸ m/s = λ ^. 1.74 x 10¹⁷ Hz
λ = 1.72 x 10^-9 m

EXAMPLE 3: What type of electromagnetic radiation is the particle from EXAMPLE 1?
answer for wavelength is 10^-9 so use chart below to determine…
x-rays or ultraviolet (either one is acceptable)
PROBLEMS FOR YOU TO TRY ON YOUR OWN…

1.) A particle of EM radiation has a frequency of 5.76 x 10¹⁴ Hz.
(A) How much energy does this particle have?
(B) What is the wavelength of this particle?
(C) What specific type of electromagnetic radiation does this particle represent?

2.) A particle of electromagnetic radiation has 2.39 x 10^-13 Joules of energy.
(A) What is the wavelength of this particle?
(B) What type of electromagnetic radiation does this particle represent?

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Light Calculations Notes:
* Frequency and wavelength are ___________________ proportional
* Energy and frequency are ____________________ proportional

Light as a Particle Notes:
* Object emits energy in small, specific amounts (called ________________)
* _________________: particle of EM radiation carrying a quantum of energy
* Einstein suggested that light had properties of both waves and particles
   Referred to as the ________________________________________ of light

Quantum Theory Notes:
* When atom falls from excited state to ground state, _____________________________________________
_______________________________________________________________________________________
* Energy of photon = difference ______________________________________________________________
_______________________________________________________________________________________
* Energy states of atoms are fixed

Bohr model of the hydrogen atom Notes:
* said that e- circled the nucleus in fixed paths
* when in path, has fixed amount of energy
* e- cannot exist in space between path
* drawback of Bohr’s model =

EMISSION & ABSORPTION SPECTRA

According to the Bohr atomic model, electrons orbit the nucleus within specific energy levels.  These levels are defined by unique amounts of energy.  Electrons possessing the lowest energy are found in the levels closest to the nucleus.  Electrons with higher energy are located in progressively more distant energy levels.

If an electron absorbs sufficient energy to bridge the "gap" between energy levels, the electron may jump to a higher level.  Since this change results in a vacant lower orbital, this configuration is unstable.  The "excited" electron releases its newly acquired energy as it falls back to its initial or ground state.  Often, the excited electrons acquire sufficient energy to make several energy level transitions.  When these electrons return to the ground state, several distinct energy emissions occur.  The energy that the electrons absorb is often of a thermal or electrical nature, and the energy that an electron emits when returning to the ground state is called electromagnetic radiation.

In 1900, Max Planck studied visible emissions from hot glowing solids.  He proposed that light was emitted in "packets" of energy called quanta, and that the energy of each packet was proportional to the frequency of the light wave.  According to Einstein and Planck, the energy of the packet could be expressed as the product of the frequency (n) of emitted light and Planck's constant (h).  The equation is written as        E = hn

If white light passes through a prism or diffraction grating, its component wavelengths are bent at different angles.  This process produces a rainbow of distinct colors known as a continuous spectrum.  If, however, the light emitted from hot gases or energized ions is viewed in a similar manner, isolated bands of color are observed.  These bands form characteristic patterns - unique to each element.  They are known as bright line spectra or emission spectra.

By analyzing the emission spectrum of hydrogen gas, Bohr was able to calculate the energy content of the major electron levels.  Although the electron structure as suggested by his planetary model has been modified according to modern quantum theory, his description and analysis of spectral emission lines are still valid.

In addition to the fundamental role of spectroscopy played in the development of today's atomic model, this technique can also be used in the identification of elements.  Since the atoms of each element contain unique arrangements of electrons, emission lines can be used as spectral fingerprints.  Even without a spectroscope, this type of identification is possible since the major spectral lines will alter the color.

ELECTRON ARRANGEMENT

Heisenberg Uncertainty Principle:

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GENERAL LOCATION -------------------- ____________________

|

V

____________________

|

V

____________________

|

V

SPECIFIC LOCATION -------------------- ____________________

ENERGY LEVELS - divisions of the electron cloud

- numbered consecutively from closest to farthest away from nucleus

.

Electrons will occupy the location with the lowest amount of energy.

SUBLEVELS - divisions of energy levels

- designated by letters (s, p, d, f)

- number of sublevels in an energy level = # of the energy level

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ORBITALS - divisions of sublevels

- number of orbitals in an energy level =

- “s” sublevel has 1 orbital; “p” sublevel has 3 orbitals; “d” sublevel has 5 orbitals;
“f” sublevel has 7 orbitals

HOW MANY ELECTRONS CAN AN ORBITAL HOLD?

HOW MANY ELECTRONS CAN EACH SUBLEVEL HOLD?
“s” = ___ e- “p” = ___ e- “d” = ___ e- “f” = ___ e-

HOW MANY ELECTRONS CAN AN ENERGY LEVEL HOLD?

AUFBAU PRINCIPLE –

What is the order in which the sublevels fill with electrons? Use the DIAGONAL RULE.

1s

2s 2p

3s 3p 3d

4s 4p 4d 4f

5s 5p 5d 5f

6s 6p 6d 6f

7s 7p

More Electron Arrangement!

Examples:

Se 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁴

Sn 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p²

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

HOEL (Highest Occupied Energy Level): energy level furthest from the nucleus that contains at least one electron

How to determine this using electron configuration?

~ largest non-exponent number

Se 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁴ HOEL = 4

Sn 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p² HOEL = 5

Hg 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s² 4f¹⁴ 5d¹⁰ HOEL = 6

Valence Electrons: electrons in the HOEL

How to determine this using electron configuration?

~ add up exponents of terms in HOEL

Se 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁴
HOEL = 4 Valence electrons = 2 + 4 = 6

Sn 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p²
HOEL = 5 Valence electrons = 2 + 2 = 4

Hg 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s² 4f¹⁴ 5d¹⁰
HOEL = 6 Valence electrons = 2

Noble Gas Configuration: shortcut for electron configuration

How is it written?

~ [ symbol for noble has closest to element with lower atomic # ]

~ [after brackets] next number is the period that the element is located in

~ after that number, write “s”

~ continue electron configuration in diagonal rule order until appropriate # of
electrons is reached

*NOTE: ending of electron configuration and noble gas configuration should be the same*

Se 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁴
[Ar] 4s² 3d¹⁰ 4p⁴

^{18 20 30 34}

Sn 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p²

[Kr] 5s² 4d¹⁰ 5p²

^{36 38 48 50}

Hg 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s² 4f¹⁴ 5d¹⁰
[Xe] 6s² 4f¹⁴ 5d¹⁰

^{54 56 70 80}

Orbital Notation: drawing of how electrons are arranged in orbitals; will only need to do this for the HOEL

*NOTE: ___ = orbital or = electrons

Se 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁴
Sn 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p²

Hg 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s² 4f¹⁴ 5d¹⁰
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Dot Diagrams: symbol represents nucleus and non-valence (“inner-shell”) electrons; dots around symbol represent valence electrons

QUANTUM NUMBERS
~ describe one specific electron
~ 1st quantum number = PRINCIPAL QUANTUM NUMBER
            ~ abbreviated "n"
            ~ tells the energy level the electron is located in
            ~ n = number of the energy level
            ~ 1st energy level: n = 1, 4th energy level: n = 4, etc.

~ 2nd quantum number = ANGULAR MOMENTUM QUANTUM NUMBER
~ abbreviated " l "
~ tells the sublevel the electron is located in
~ tells shape of orbital
~ "s" sublevel: l = 0, "p" sublevel: l = 1, "d" sublevel: l = 2, "f" sublevel: l = 3

~ 3rd quantum number = MAGNETIC QUANTUM NUMBER
~ abbreviated "m"
~ tells which orbital the electron is in
~ tells orientation of orbital around nucleus
~ m = - l .. + l

~ 4th quantum number = SPIN QUANTUM NUMBER
~ abbreviated " s "
~ tells which electron is being described
~ tells which way electron is spinning
~ s = -¹/₂ or +¹/₂

Pauli Exclusion Principle:

EXAMPLE QUESTIONS:
1.) What are the 4 quantum numbers for the following electron? h
3 p

2.) If the electron in question 1 was the last electron added, what element would it be?

3.) Draw in the electron (and the orbital notation) for the electron with the following quantum numbers.
n = 3 l = 2 m = -1 s = - ½

4.) How many electrons in an atom can have the quantum numbers n = 3 and l = 1?

5.) What are the four quantum numbers for the electron circled in the diagram below?
n = l = m = s =

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