# Energy Levels and Orbitals

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Energy Levels and Orbitals
An investigation into electrons and their location and behavior within the atom Learning Targets: Describe the process of excitation and emission of energy by an electron. Understand what each quantum number represents and how they are determined – energy level, subshell, orbital, and spin.

Emission Spectroscopy
The spectra that were shown through emission spectroscopy led Niels Bohr to question the structure of the atom.

Emission Spectroscopy
With white light, all of the colors of the visible spectrum are shown.

Emission Spectroscopy
Since that was NOT what the spectra of elements looked like, Bohr began to look at why only certain wavelengths of color appeared.

Emission Spectroscopy
E = hc λ Energy h = 6.63 x Js wavelength c = speed of light This equation shows that larger wavelengths indicate lower amounts of energy and smaller wavelengths indicate higher amounts of energy... an inverse relationship. Bohr realized that the specific wavelengths revealed specific amounts of energy.

Emission Spectroscopy
Specific amounts of energy!! That inferred that energy within the atom existed at specific amounts. Bohr called these orbits, or energy levels. An electron cannot be in-between energy levels, it can only be within an energy level. Therefore, energy is quantized. The Bohr Model

Emission Spectroscopy
Bohr realized that the spectra were being created as electrons moved between these energy levels: If an electron absorbs energy, it may jump to a higher energy level. When an electron is at a higher energy level we say that the electron is in its “excited” state. When the electron releases energy in the form of radiation, we say that the electron has returned to its “ground” state. The type of radiation that is emitted depends on the amount of energy released.

Emission Spectroscopy
The Bohr Model When energy enters the atom, an electron (shown in red) can absorb the energy becoming excited, AND jumping to higher energy levels. 4th Energy Level 1st Energy Level Energy Coming In! Nucleus 3rd Energy Level 2nd Energy Level

Emission Spectroscopy
The Bohr Model When the electron releases the energy, the electron returns to lower energy levels. Other forms of electromagnetic radiation, besides visible light, can be emitted. 4th Energy Level 1st Energy Level Energy emitted (ultraviolet light) Nucleus Energy emitted (red light) Energy emitted (infrared) 3rd Energy Level 2nd Energy Level

Emission Spectroscopy
The Bohr Model When the electron returns to its ground state, it has the option of jumping down multiple energy levels, rather than one at a time. 4th Energy Level 1st Energy Level Energy emitted (ultraviolet light) Nucleus Energy emitted (blue/green light) 3rd Energy Level 2nd Energy Level

Emission Spectroscopy
The Bohr Model Since a sample of gas has many atoms, there are many electrons. This is why Bohr saw multiple colors. But there were other electromagnetic waves, too. 4th Energy Level 1st Energy Level Nucleus Energy emitted (red light) Energy emitted (blue/green light) 3rd Energy Level 2nd Energy Level

Emission Spectroscopy
This is the full electromagnetic spectrum.

Emission Spectroscopy
Electromagnetic Waves Bohr saw Visible Light: wavelength is in the range of 400 to 700 nanometers (4 x 10-7 meters) ROY G. BIV White light is made of all the colors of light

Emission Spectroscopy
Electromagnetic Waves Gamma rays: cosmic radiation, very high energy Ultraviolet rays (UV): solar radiation, high energy Infrared rays (IR): thermal radiation, remote controls, low energy Microwave rays: microwave oven, very low energy

Emission Spectroscopy
Electrons release certain types of electromagnetic radiation as they fall to specific lower energy levels. Energy Level Change Spectra Emission 2 --> 1 Ultraviolet 3 --> 1 Ultraviolet 4 --> 1 Ultraviolet 3 --> 2 Visible Red 4 --> 2 Visible Blue/Green 5 --> 2 Visible Blue 4 --> 3 Infrared

Quantum Mechanical Model
In addition to knowing that there were energy levels in the atom, three scientists began to notice other things... Heisenberg – impossible to know the exact position and exact speed of an electron at the same time De Broglie – electrons have wave-like properties, as in they move in wave patterns Schroedinger – developed probability of finding each electron in a given location

Quantum Mechanical Model
Heisenberg Bohr suggested that the electrons move in perfect circles around the nucleus. Heisenberg showed that, instead, the electron moves in a three dimensional cloud of probability that is smeared out over the orbit – Heisenberg uncertainty principle

Quantum Mechanical Model
DeBroglie Bohr suggested that the electrons move in perfect circles around the nucleus. DeBroglie showed that there were other shapes because the electrons moved like waves – wave-particle duality.

Quantum Mechanical Model

Quantum Mechanical Model
Schrodinger Schroedinger realized how to put the theories of Bohr, Heisenberg, and DeBroglie together by creating a mathematical equation to find the most likely location for each electron within an atom – wave equation. Watch this YouTube video.

Quantum Mechanical Model
Every electron within an atom has “coordinates”. Schrodinger gave these coordinates numerical values, known as quantum numbers. Each quantum number describes part of the coordinates that determine the energy and probable location of any electron for any atom.

Quantum Mechanical Model
First Quantum Number  Energy Level Energy levels begin at the number 1. Each level is higher in energy than the next. The higher in energy, the farther away from the nucleus.

Quantum Mechanical Model
Second Quantum Number  Subshell Atoms are three dimensional. Within the energy levels exist different shapes, or subshells. The shapes are determined by how much energy is required to create them.

Quantum Mechanical Model
Second Quantum Number  Subshell There are four main shapes: s, p, d, and f. s – think sphere p – think peanut d – think daisy f – think fireburst

Second Quantum Number  Subshell

Quantum Mechanical Model
Second Quantum Number  Subshell Since the subshells are determined by how much energy is required to create them, lower energy levels have fewer subshells. (The lower the energy level, the lower the energy.) The 1st energy level can only contain the s subshell. A simple sphere does not take a lot of energy to create.

Quantum Mechanical Model
Second Quantum Number  Subshell The higher the energy level, the more subshells can be held. The 2nd energy level can contain the s and the p subshell. As Bohr suggested, these subshells are further away from the nucleus.

Quantum Mechanical Model
Second Quantum Number  Subshell The 3rd energy level must contain three subshells - the s, p, and d. In effect, the numeric value that represents the energy level also represents the number of subshells within that energy level.

Quantum Mechanical Model
To recap: Energy level 1 = 1 subshell (s) Energy level 2 = 2 subshells (s and p) Energy level 3 = 3 subshells (s, p, and d) Energy level 4 = 4 subshells (s, p, d, and f) etc. Why are more subshells present? Each energy level is larger than the previous. As a result, there are more possible locations for where an electron could reside.

Quantum Mechanical Model
Nucleus 1s subshell 2s subshell 2p subshell 3s subshell 3p subshell

Quantum Mechanical Model
3d subshell 4s subshell

Quantum Mechanical Model

Quantum Mechanical Model
Third Quantum Number  Orbitals Did you notice that there were different positions of some of the subshells? The different positions, or orientations, are called orbitals, not orbits. The orbitals are determined by which subshell they are in and in which positions they are. The s orbital does NOT have a different position. The p orbital has THREE different orientations – x, y, and z.

Quantum Mechanical Model
Third Quantum Number  Orbitals Each orbital has a specific number of locations on the x, y, z axes. - s has 1 orbital orientation (just s) - p has 3 orbital orientations (px, py, pz) - d has 5 orbital orientations (dxy, dxz, dyz, dz2, dx2-y2) - f has 7 orbital orientations (too complex to list)

Quantum Mechanical Model
Third Quantum Number  Orbitals If the next subshell is called “g”, how many orbital orientations should it have? _________ After “g” the next subshell would be “h”. How many orbital orientations should it have? 9 11

Third Quantum Number  Orbitals
There is 1 s orbital There are 3 p orbitals There are 5 d orbitals There are 7 f orbitals

Quantum Mechanical Model
Fourth Quantum Number  Electron Spin Each electron can be spin up (+1/2) or spin down (-1/2) No two electrons in the same orbital orientation can have the same spin. With only one spin up and one spin down, the maximum number of electrons that can fit into any given orbital orientation is two. This is called the Pauli Exclusion Principle.

Quantum Mechanical Model
Let’s put it all together!

Quantum Mechanical Model
Energy Level Possible Subshells Atomic Orbitals Number of Electrons in Each Subshell Maximum Possible Electrons in Energy Level 1 s 2 p 3 6 8 d 5 10 18 4 f 7 14 32