Chapter 5: Electrons in Atoms Revising the Atomic Model Atomic Emission Spectra and the Quantum Mechanical Model

Learning Target You will identify You will identify the energy level, sublevel, orbital, and spin of an electron in an atom.

Previous Atom Models You will identify the energy level, sublevel, orbital, and spin of an electron in an atom.

Quantum Mechanical Model Austrian physicist Erwin Schrödinger (1887–1961) used new theoretical calculations and experimental results to devise and solve a mathematical equation describing the behavior of the electron in a hydrogen atom. The modern description of the electrons in atoms, the quantum mechanical model, came from the mathematical solutions to the Schrödinger equation. You will identify the energy level, sublevel, orbital, and spin of an electron in an atom.

Quantum Mechanical Model Like the Bohr model, the quantum mechanical model of the atom restricts the energy of electrons to certain values. Unlike the Bohr model, however, the quantum mechanical model does not specify an exact path the electron takes around the nucleus. You will identify the energy level, sublevel, orbital, and spin of an electron in an atom.

Sublevels and Orbitals Solutions to the Schrödinger equation give the energies, or energy levels, an electron can have. Each of these levels is divided into sublevels. (s, p, d and f) For each energy level, the Schrödinger equation also leads to a mathematical expression, called an atomic orbital. An atomic orbital is represented pictorially as a region of space in which there is a high probability of finding an electron. You will identify the energy level, sublevel, orbital, and spin of an electron in an atom.

Sublevel pictures S sublevel You will identify the energy level, sublevel, orbital, and spin of an electron in an atom.

Summary of energy levels and sublevels Principal quantum number, n, = # of sublevels w/in that principal energy level. # of orbitals in a principal energy level = n 2. A max of 2 electrons can occupy an orbital. Therefore, the maximum number of electrons that can occupy a principal energy level is given by the formula 2n 2. Example: Calculate the maximum number of electrons in the 5 th principal energy level (n = 5). The maximum number of electrons that can occupy a principal energy level is given by the formula 2n 2. If n = 5, 2n 2 = 50. You will identify the energy level, sublevel, orbital, and spin of an electron in an atom.

Summary of energy levels and sublevels Principal Energy Level Number of sublevels Type of sublevelMaximum number of electrons n = 111s (1 orbital)2 n = 222s (1 orbital), 2p (3 orbitals) 8 n = 333s (1 orbital), 3p (3 orbitals), 3d (5 orbitals) 18 n = 444s (1 orbital), 4p (3 orbitals), 4d (5 orbitals), 4f (7 orbitals) 32 You will identify the energy level, sublevel, orbital, and spin of an electron in an atom.

s sublevel label and draw You will identify the energy level, sublevel, orbital, and spin of an electron in an atom.

p sublevel label and draw You will identify the energy level, sublevel, orbital, and spin of an electron in an atom.

d sublevel label and draw You will identify the energy level, sublevel, orbital, and spin of an electron in an atom.

f sublevel label and draw You will identify the energy level, sublevel, orbital, and spin of an electron in an atom.

Energy Levels-Label on YOUR periodic table You will identify the energy level, sublevel, orbital, and spin of an electron in an atom.

Nature of Light By the year 1900, there was enough experimental evidence to convince scientists that light consisted of waves. The amplitude of a wave is the wave’s height from zero to the crest. The wavelength, represented by λ (the Greek letter lambda), is the distance between the crests. The frequency, represented by ν (the Greek letter nu), is the number of wave cycles to pass a given point per unit of time. The SI unit of cycles per second is called the hertz (Hz).

Classes of EM Radiation Electromagnetic radiation includes radio waves, microwaves, infrared waves, visible light, ultraviolet waves, X-rays, and gamma rays. All electromagnetic waves travel in a vacuum at the speed of light.

c = λ · ν c - speed – speed of light (3.0 x 10 8 m/s) λ - wavelength - the distance between two waves(must be in m) ν - frequency – the number of waves that pass a given point per unit of time (Hz or s -1 ) (Hz is hertz)

E = h · ν Planck recognized energy is quantized and related the energy of radiation to its frequency E = energy in J h = Planck’s constant (6.626 x J s) v = frequency (Hz or s -1 )

Examples of problems “The wavelength of green light is about 522 nm. What is the frequency of this radiation?” “What is the energy of a photon with a wavelength of 827 nm?”

Example #1 “The wavelength of green light is about 522 nm. What is the frequency of this radiation?” Wavelength – given (needs to be in meters!) Frequency - ? What equation has wavelength and frequency? c = λ x ν

Example #1 Cont. “The wavelength of green light is about 522 nm. What is the frequency of this radiation?” c = λ x ν Solving for v in this equation so c / λ = v (3.0 x 10 8 m/s) / (5.22 x m) = 5.75 x Hz or s -1

Example #2 “What is the energy of a photon with a wavelength of 827 nm?” Wavelength – given Energy - ? What equation has energy and wavelength? E = h x ν c = λ x ν

Example #2 cont. “What is the energy of a photon with a wavelength of 827 nm?” E = h x ν c = λ x ν Solving for energy so equation but need to find v first c / λ = v  (3.0 x 10 8 m/s)/(8.27 x m) = 3.63 x Hz or s -1

Example #2 cont. “What is the energy of a photon with a wavelength of 827 nm?” E = h x ν c = λ x ν Now put frequency into energy equation E = h x ν  (6.626 x J s) x (3.63 x Hz or s -1 ) = 2.40 x J

Homework Electromagnetic Spectrum Worksheet #2