1. Warm Up
A new element, Tyserium (Ty), has recently been discovered and consists of two isotopes. One isotope has a mass of 331 g/mol and is % abundant. The other isotope is 337 g/mole and is 65.0 % abundant. What is the mass of Ty as it appears on the periodic table?

2. Givens
35.0% is 331 g/mol
65.0% 337 g/mol
Step 1
Mass abundant
(.350)(331g/mol)=116g/mol
(.650)(337g/mol)=219g/mol

3. Step 2 Weighted avg
116g/mol +219 g/mol =
335 g/mol

4. Light and Quantum Theory
Supplement Chemquest 10 and 11

5. Waves and Light
The quantum mechanical model of the atom is based on the study of waves and light. Important wave definitions and relationships: amplitude – the distance from the crest to the midway origin line of the wave.

6. Waves and Light
wavelength (, the Greek letter lambda) – the distance between similar points in a set of waves, such as crest to crest or trough to trough; normally expressed in a meter- type unit. frequency (, the Greek letter nu) – the number of waves that pass a given point per unit time; usually expressed in cycles/second (sec-1 or 1/sec), commonly known as Hertz, Hz.

7. Waves and Light
Frequency, wavelength, and energy are related to one another mathematically through: c =  and E = h where “c” is the speed of light (3.00x108 m/s) and “h” is Planck’s constant (6.626x10-34 J/Hz). (Watch for unitary agreement!) Inspection of these relationships suggests that frequency and wavelength are inversely proportional and that energy and frequency are directly proportional.

8. Waves and Light
Electromagnetic Radiation (EMR) – a form of energy that travels in waves. The EMR spectrum includes all visible light and many other forms of wave energy:

9. Waves and Light
Fill in these blanks for the EMR spectrum: The highest energy visible light is violet light. The lowest energy waves in the EMR spectrum are radiowaves. Visible red light has shorter wavelength than infrared light. Visible green light has lower energy than Xrays. Visible indigo light has lower frequency than ultraviolet light.

10. Waves and Light
EMR travels at the speed of light in a vacuum, 3.00x108 m/s. Types of EMR differ from each other by wavelength, frequency, and resulting energy. All EMR is the result of electron movement between energy levels within atoms. When an electron moves to a higher energy level, farther from the nucleus, energy is consumed and the atom is referred to as “excited”. As the electron returns to a lower energy level, energy is emitted in the form of photons discrete packets of radiant energy that travel in waves (suggested by Einstein).

11. Waves and Light
Because of unique arrangements of electrons within atoms, each element has a characteristic light it emits when exposed to a sufficient amount of heat or electricity. When examined through a spectrophotometer, a device that breaks light into its component waves, the element’s bright-line spectrum is observed. (See p.126 for the BLS for hydrogen.) A BLS is not a continuous spectrum like the EMR spectrum, but it is distinct lines of color that correspond to very specific wavelengths, frequencies, and energies. The energies correspond to the energies required to move electrons farther from the nucleus and that emitted when they return to their original locations.

12. Waves and Light
Elements also have unique and specific energy requirements to completely remove an electron from an atom. Ionization energy is the amount of energy required to remove an electron from a gaseous atom of an element. The energy required is equal to the energy emitted when an electron is added to an atom from some other source. Of course, ionization energy is greater than the various energies required or emitted as electrons move within an atom.

13. The Quantum Mechanical Model
Work to relate wave behavior, atomic energy levels, and electrons by Louis deBroglie and Erwin Schrodinger led to the branch of physics called quantum mechanics. Quantum mechanics and probability, the statistical likelihood of an occurrence, are the basis for current atomic models. Electrons are particles with wave characteristics. Probability helps describe the behaviors and positions of electrons. One important assumption of today’s model is the Heisenberg Uncertainty Principle which states that it is not possible to describe both position and speed of an electron at the same point in time.

14. The Quantum Mechanical Model
An important distinction to make is that between an orbit (a pathway, as in Bohr’s Model of the atom) and an orbital. An orbital is a region of space around a nucleus in which an electron is most likely to be found. It is not a barrier or pathway, only a model describing the likely occupied area.

15. The Quantum Mechanical Model
Schrodinger developed a mathematical model for the wave behavior of an electron.
The very complex equation contains four quantum numbers that are used to describe electron location and behavior…

16. The Quantum Mechanical Model

17. The Quantum Mechanical Model
n Principle Quantum Number
refers to the energy level location of the electron
n is 1,2,3,4,… n (up to 7)
the number of sublevels in the energy level = n (up to 4)
the number of available orbitals in the energy level = n2 (up to 16)
the greatest number of electrons contained in any one energy level = 2n2 (up to 32). Ex: where n=3, the maximum number of electrons is 2(3)2 = 18.

18. The Quantum Mechanical Model
l  Azimuthal or Orbital Quantum Number
refers to the sublevel location of the electron
l is either s, p, d, or f
s-sublevel orbitals are spherical in shape. They are closest to the nucleus; thus electrons located here have the lowest relative energies within the energy level. There is only 1 s-orbital per energy level.

19. The Quantum Mechanical Model
p-sublevel orbitals are dumbbell-shaped. They are a little farther from the nucleus; thus electrons located here have a little higher relative energies within the energy level. There are 3 p-orbitals (px, py, pz) per energy level, starting with energy level 2.

20. The Quantum Mechanical Model
d-sublevel orbitals are cloverleaf-shaped, very complex. They are even a little farther from the nucleus; thus electrons located here have even higher relative energies within the energy level. There are 5 d-orbitals per energy level, starting with energy level 3.

21. The Quantum Mechanical Model
f-sublevel orbitals are extremely complex in shape. They are farthest from the nucleus; thus electrons located here have the highest relative energies within the energy level. There are 7 f-orbitals per energy level, starting with energy level 4.

22. The Quantum Mechanical Model
ml Magnetic Quantum Number
designates the number of orbitals on each sublevel and in which specific orbital the electron is likely located
describes the home orbital’s geometric orientation about the x, y, and z axes

23. The Quantum Mechanical Model
ms  Spin Quantum Number
describes the direction of spin for the electron
ms is either +1/2 (clockwise spin) or –1/2 (counter- clockwise spin).
The Pauli Exclusion Principle is very important here and throughout the quantum model. It states that:
1) no more than 2 electrons may occupy any one orbital;
2) if electrons occupy the same orbital, they must have opposite spin directions;
3) thus, no two electrons in one atom will have all four quantum numbers identical.

24. The Quantum Mechanical Model
ms is either +1/2 (clockwise spin) or –1/2 (counter-clockwise spin)
The Pauli Exclusion Principle
3p____ _______ _______ X no more than 2 electrons may occupy any one orbital
3p _____ _____ ________ if electrons occupy the same orbital, they must have opposite spin directions;
3p _____ _____ ________ X