Chapter 07: The Quantum-Mechanical Model of the Atom Flashcards
Light
A form of electromagnetic radiation
Composed of perpendicular oscillating waves
(one = electric field, other = magnetic field)
Electric field
A region where an electrically charged particle experiences a force
Magnetic field
A region where a magnetized perticle experiences a force
Speed of light
c
c = 3.00 × 108 m/s
Wavelength
λ (lambda)
The distance between identical points on successive waves
*Inversely proportional to frequency
Amplitude
The verticle distance from the midline of a wave to the peak (or trough)
A measure of light intensity
*Directly proportional to total energy of wave
(larger amplitude = more force)
Frequency
- v* (nu)
- v* = c / λ
The number of waves that pass through a particular point in a given period of time
hertz (Hz) or cycles per second (1 s-1)
1 Hz = 1 s-1
*Directly proportional to total energy of a wave
(More frequency = more total force)
*Inversely proportional to wavelenth
Electromagnetic spectrum
Low energy to high:
radio
microwave
infared
visible light
ultraviolet
X-ray
gamma ray
Interference
The interaction between waves
Constructive interference
Occurs when waves that are in phase interact so that they add to make a larger wave
*Amplitudes are summed making the larger wave
Destructive interference
Occurs when waves that are out of phase interact so that they cancel each other out (flat line)
Diffraction
Occurs when a traveling wave encounters an obstacle or opening in a barrier that is about the same size as its wavelengh and it bends (diffracts) around it
*Waves diffract
**Particles DO NOT diffract (they just pass through opening)
Interference pattern
Inherent characteristic of all waves
Light is diffracted through two slits creating an alternating pattern
Photoelectric effect
The observation that many metals emit electrons when light shines on their surface
Quanta or photons
Light energy delivered to atoms in “packets”
Photon energy
E
E = hv
v = c/λ
Thus:
E = hc/λ
Planck’s constant
h
h = 6.626 × 10-34 J×s
Threshold frequency
Reached when the energy of a photon is equal to the binding energy of emitted electron
hv = Φ
or E = Φ
Binding energy of emitted electron
Φ (phi)
Kinetic energy of an ejected electron
KE = hv - Φ
Excess energy of a photon that is transferred to an electron in the form of kinetic energy
Wave-particle duality of light
Sometimes light appears to behave like a wave, other times like a particle
Behavior observed depends on experiment
Number of photons
Number of photons = Epulse / Ephoton
*Ephoton = hc/λ
Atomic spectroscopy
The study of the electromagnetic radiation absorbed and emitted by atoms
Emission spectrum
The “fingerprint” of an element in the form of a series of bright lines
Can be used to identify an element
Bohr model of the atom (4)
- Energy of atom is quantized (can only have very specific amounts of energy
- Amount of energy in atom relates to electron’s position in atom
- Electrons travel in orbits/fixed distance from nucleus
*Energy of electron proportional to distance - Electrons emit radiation when they “jump” from an orbit with higher energy down to lower energy orbit
*Distance determins energy of photon of light produced
de Broglie relation
Wavelength inversely proportional to momentum (mv)
λ = h/mv
(Wavelength = h/mass * frequency)
Complimentary properties
The more you know about one property, the less you know about the other
When wave nature (interference pattern) is observed, particle nature (position/which slit electron passes through) cannot be, and vice versa
Heisenberg uncertainty principle
Product of uncertainties in both position and speed of a particle is inversely proportional to its mass
Δx × mΔv ≥ h/4π
Δx = position uncertainty
Δv = velocity uncertainty
m = mass
Indeterminacy
Indefinite future = can only predict probability
Orbital
A probability distribution map of a region where the electron is likely to be found
Quantum numbers (4)
- Principal quantum number, n
- Angular momentum quantum number, l
- Magnetic quantum number, ml
- Spin quantum number, ms
Principal quantum number
n
Indicates the orbital (Bohr’s energy level)
*As n gets larger, amount of energy between orbitals gets smaller
Equation for energy of a hydrogen electron
En = -R<em>H</em> (1/n2)
R<em>H</em> is Rydberg constant for hydrogen
R<em>H</em> = 2.18 × 10-18 J
Angular momentum quantum number
l
Angular momentum = what kind of/angle of orbit
l = 0, 1,… n-1
l = 0 → s l = 1 → p l = 2 → d l = 3 → f
e.g.
n = 2
l = [0, 1]
Magnetic quantum number
ml
ml = [-l, l]
e.g.
n = 2
l = [0, 2] → d orbital
ml = [-2, 2] → 5 d orbitals
Spin quantum number
ms
Specifies the orientation of the spin of the electron
Value is either:
+1/2 (spins up)
or
-1/2 (spins down)
Describing an orbital (3)
- n, l, ml describes one orbital
- Orbitals with same n value = same principal energy level (shell)
- Orbitals with the same values of n & l = same sublevel (subshell)
Equation for energy transition in hydrogen
ΔE = Efinal - Einitial
ΔEH atom = -2.18 × 10-18 J (1/n2final - 1/n2initial)
Energy emitted by electron is carried away by the releated photon, thus:
Ephoton = -ΔE
Probability density
The probability of finding an electron at a particular point in space
Probability decreases as distance from nucleus increases
Radial distribution function
Total probability of finding an electron at a certain distance r from the nucleus
Volume of shell also increases with distance from nucleus
Nodes
Where the probability drops to zero, for both probabilities
s orbital
l = 0
spherical shape
1 s orbital
p orbital
l = 1
shaped like two balloons
-1, 0, 1
3 p orbitals
d orbital
l = 2
shaped like four balloons
-2, -1, 0, 1, 2
5 d orbitals
f orbital
l = 3
shaped like eight balloons
-3, -2, -1, 0, 1, 2, 3
7 f orbitals
