Chemistry A Molecular Approach AP Edition Chapter 7

Chapter 7: The Quantum-Mechanical Model of the Atom 

7.1 Schrodinger's Cat

• Atoms and the particles that make up atoms are very very small. Electrons are so small that they cannot be measured. 
• The absolute small, or quantum, world of an electron behaves differently than the world we are used to observing. 
• Electrons can be in two different states at the same time. We are used to observing things that are only in one state at a time.
• Trying to measure an electron forces it into one state or another
• Erwin Schrodinger tried to explain the quantum world through an experiment with a cat. If you put a cat in a box with deadly chemicals, the cat can be both dead and alive. But once you remove the box, it can only be either dead or alive. 
• The quantum mechanical model of the atom explains the behavior of electrons and why some have certain properties 

7.2 The Nature of Light 

• Light has many characteristics of electrons 
• The most common characteristic was the wave-particle duality of light. This is when some properties are best described as a wave and other properties are better described as a particle  

The Wave Nature of Light: 

• Light is electromagnetic radiation. A magnetic field is where magnetic particles experience force and an electric field is where electrically charged particles experience force. 
• Light travels much faster than sound 
• A wave can be characterized by the amplitude and the wavelength
• Amplitude is the vertical height of a crest. In light, it determines the brightness or intensity 
• A wavelength (λ) is the distance between adjacent crests. Wavelengths can be measure in meters, micrometers, or nanometers 
• Light is also characterized by frequency (v). Frequency is the number of cycles that pass through a certain point at any period of time. The unit of frequency is s^-1
• c is the speed of light 
• v= c/λ
• In visible light, the wavelength determines color. Reds have the longest wavelengths while violets have the shortest 

The Electromagnetic Spectrum:

• The electromagnetic spectrum includes all wavelengths of electromagnetic radiation. It ranges from gamma rays to radio waves 
• Short wavelengths use more energy than long wavelengths
• Gamma rays have the shortest wavelengths. The are produced by the sun, stars, and unstable atomic nuclei. Exposure to gamma rays can be extremely harmful 
• X-rays are typically used in the medical field. The have slightly longer wavelengths than gamma rays. X-rays can pass through substances that block visible light. Too many X-rays can be harmful 
• After X-rays comes ultraviolet radiation (UV). This light comes from the sun and is what causes sunburns. Excessive exposure to UV rays can cause skin cancer. 
• Visible light ranges from the short wavelengths of violet to the long wavelengths of red. They cannot cause damage to our biological molecules. 
• After visible light comes infrared radiation (IR). This is the heat you feel when you place your hand near a hot object. All warm objects will emit IR light. 
• After IR comes microwaves. They are used in microwave ovens.
• Radio waves have the longest wavelengths. They transmit signals from AM and FM radio, cellular telephones, and televisions.  

Interference and Diffraction:

• Waves can either cancel eachother out or build each other up. This interaction is referred to as interference. 
• When waves are in phase when they interact, a wave twice the amplitude will be created. This is known as constructive interference 
• When waves are out of phase, the waves cancel out. This is called destructive interference 
• When a wave encounters and objects that is a comparable size to the wavelength, is bends around it. This bending is referred to as diffraction 

The Particle Nature of Light: 

• The photoelectric effects is an observation that many metals emit electrons when light is shines on them. Only the amplitude of light affects the emission of electrons, not the wavelength 
• The rate at which electrons leave the metal increases with the increasing of the intensity of the light 
• Low frequency light does not eject electrons but high frequency light does 
• h is Planck's constant 
• A packet of light is called a photon 
• The amount of energy in a light packet can be found using these equations 
• E = hv
• E = hc/λ

7.3 Atomic Spectroscopy and the Bohr Model

• Atomic spectroscopy is the study of electromagnetic radiation absorbed and emitted by atoms 
• When an atom absorbs energy, it re-emits that energy as light
• A series of bright lines is called an emission spectrum. This spectrum can be used to classify elements 
• Niels Bohr developed a model to explain the atomic spectra. Electrons travel around the nucleus in a circular orbit. These orbits only exist in fixed distances from the nucleus. The energy of each orbit is also fixed.  

7.4 The Wave Nature of Matter: The de Broglie Wavelength, the Uncertainty Principle, and Indeterminacy 

• Electrons also have a wave nature. This nature is most clearly seen in the fact that electrons can diffraction.
• Electron interference is caused by electrons interfering with themselves. 

The de Broglie Wavelength:

• An electron's wavelength is related to its kinetic energy
• The faster an electron is moving, the higher its kinetic energy and the shorter its wavelength. 
• de Broglie relation is expressed by the equation λ = h/mv

The Uncertainty Principle: 

• "We can never see the interference pattern and simultaneously determine which hole the electron goes through"
• Wave nature and particle nature are complementary properties 
• The more we know about one property, the less we know about the other 
• The velocity of an electron relates to its wave nature
• The position of an electron relates to its particle nature 
• We cannot simultaneously measure an electron's position and velocity 
• Δ x is the uncertainty position 
• Δ v is the uncertainty velocity 
• m is the mass of the particle
• h is Planck's constant
• Heisenberg's uncertainty principle can be expressed through the following equation: Δ x X mΔ v ≥ h/4π
• The more accurate you know the position, the less accurate you know the velocity and vice versa 

Indeterminacy and Probability Distribution Maps:

• Particles move in a trajectory that is determined by a particle's velocity, position, and forces acting on it
• According to Newton's laws, the present determines the future (deterministic) 
• We cannot know the trajectory of an electron. Trajectories are replaced with probability distribution maps. These are statistical maps that show where electrons are likely to be found under certain sets of conditions 
• Indeterminacy is when you cannot determine where an electron will land because it goes somewhere different each time 

7.5 Quantum Mechanics and the Atom

• Position and energy are also complementary properties 
• An electron's position is described in terms of an orbital 

Solutions to the Schrodinger Equation for the Hydrogen Atom:

• There are many solutions to Schrodinger's equation, therefore there are many possible wave functions
• Orbitals correspond to wave functions
• There are three interrelated quantum numbers. They all have integer numbers 
• n is the principal quantum number
• l is the angular momentum quantum number 
• m_l is the magnetic quantum number
• m_s is the spin quantum number. It specifies the orientation of the spin of the electron
• The principal quantum number is an integer that determines the size and energy of an orbital. n = 1, 2, 3.... 
• E_n = -2.18 x 10^-18 J (1/n²)
• -2.18 x 10^-18 J is the Rydberg constant for hydrogen 
• Orbitals with higher values of n have greater energies. As n increases, the spacing between energy levels becomes smaller 
• The angular momentum quantum number is an integer that determines the shape of the orbital. l = 0, 1, 2…, (n - 1)
• l can be any integer up to (n - 1)
• If n = 1, l = 0
• If n = 2, l = 1 or l = 0
• The magnetic quantum number is an integer that specifies the orientation of the orbital 
• m_l are integers from -l to +l 
• If l = 1, m_l = -1, 0, or 1
• The spin quantum number specifies the orientation of the spin electron 
• All electrons have the same amount of spin 
• Spin up is when m_s = 1/2 
• Spin down is when m_s = -1/2
• Orbitals with the same n are in the same principle level/principle shell 
• Orbitals with the same n and l are in the same sublevel/subshell 

Atomic Spectroscopy Explained:

• When an atom absorbs energy, the electrons get excited. This causes them to go to a higher energy orbital 
• The electron will quickly fall back down, but will give off light as it falls 

7.6 The Shapes of Atomic Orbitals 

• Orbitals are important because covalent chemical bonds depend on the sharing of electrons that lay in the orbitals 
• The shape of overlapping orbitals determine the shape of the molecule 

s Orbitals (l = 0)

• The lowest energy level is 1s orbital 
• Probability density is the probability (per unit of volume) of finding an electron at that point 
• You are more likely to find electrons closer to the nucleus 
• The radial distribution function represents the total probability of finding the electron within a shell at a distance (r) from the nucleus 
• r = 0, the probability density is at the maximum 
• As r increases, the volume of the shell increases
• A node is when the wave function, probability density, and radial distribution function all go through 0 

p Orbitals (l = 1)

• p orbitals are not spherically symmetric. They have two lobes of electrons on either side of the nucleus
• 3p, 4p, and 5p have additional nodes and are larger in size

d Orbitals (l = 2)

• d orbitals are clover like in shape 

f Orbitals (l = 3)

• f orbitals have more lobes and nodes than d orbitals 

The Phase of Orbitals 

• The sign of an amplitude is now as its phase 
• The phase of a wave will determine how it interacts with other waves 

The Shape of Atoms

• Atoms are usually drawn as spheres