Download Section 4-2 The Quantum Model of the Atom Problems with the Bohr

Section 4-2 The Quantum Model of the Atom
Problems with the Bohr Model:
 Why did Hydrogen's electron only exist in certain specific orbits?
 Why couldn't the electron exist in limitless orbits at slightly different energies?
 Why could the model only predict the light spectrum of a single electron?
A. Electrons as Waves
I. If light is both a particle and a wave, why not electrons?
II. Louis de Broglie reasoned that electrons could interfere and diffract like light
III.Matter-Wave theory: mv/ = h (Planck's Constant) – Matter traveling fast enough becomes a
wave.
B. The Heisenberg Uncertainty Principle
I. If electrons are both particles and waves, where are they?
II. The only way to find an electron is with a photon
III.Hitting an electron with a photon changes where the electron is
IV. “It is impossible to determine simultaneously both the position and velocity of an
electron or other subatomic particle”
C. The Schrödinger Wave Equation
I. This equation defined all of the locations in an atom where electrons could and could not
exist.
II. Combined with the uncertainty principle, the wave equation defined areas of probability of
electron location
III.The “wave functions” of particular electrons are 3D regions of space that the electron could
exist in at any moment.
a. Orbitals are just probability distributions for possible electrons.
b. Every Orbital can only contain 2 electrons or less
D. Atomic Orbitals and Quantum Numbers: Q.N. Specify the properties of atomic orbitals and the
properties of electrons in the orbitals
I. Principle Quantum Number: “n”
a. Indicates the main “energy level” of the electron.
b. “n” can only be positive integers beginning with the number 1
c. As “n” increases, the electron's energy and distance from the nucleus increase
d. Multiple electrons can share a value of “n”, this is called a “shell” of electrons
e. Total possible number of orbitals in any value of “n” = n2.
II. Angular Momentum Quantum Number: “L”
a. “L” differentiates sublevels of energy.
b. “L” defines the SHAPE of the orbital occupied by the electron.
i. L = 0 is called an “S orbital” with Spherical shape
ii. L = 1 is called a “P orbital” with a Figure-8 shape
iii. L = 2 is called a “D orbital” with a double Figure-8 shape
iv. L = 3 is called an “F orbital” with a quadruple Figure-8 shape
c. The possible shapes of “L” are defined by the size of “n”
i. “L” can be any integer between 0 and (n-1).
ii. If n = 2, then L can be 0 or 1
iii. If n = 4, then L can be 0,1,2,or 3
III.Magnetic Quantum Number: “m” (sometimes “mL” in other books)
a. “m” indicates the DIRECTION of the orbital relative to the nucleus.
b. “m” can have more values as “L” increases in value
i. “m” can take on any integer value between “–L” and “+L”
ii. If “L” = 1, “m” can be –1,0,+1
iii. If “L” = 2, “m” can be –2,–1,0,+1,+2
c. Each value “m” typically has the same shape of orbital with a different rotation around
the nucleus.
IV.
Spin Quantum Number: “Spin” (sometimes “ms” in other books)
a. Every electron can either be spinning in a +½ or –½ direction
i. The + and – can be thought of as simply “up” or “down”, respectively.
b. By assigning different values of spin to electrons sharing a specific orbital, the two
identities of the two electrons are kept separate.
V. Identifying an electron with quantum numbers
a. All four quantum numbers must be known
b. No two electrons can share the exact same quantum numbers in a single atom
c. Two electrons sharing a single orbital would have the same “n”, “L”, and “m”, but have
opposite values of “Spin”.
d. Analogy: “n” is the State where you live, “L” is the county where you live, and “m” is
the ZIP code where you live – but you can share the zip code with other residents
(Different Spins)