Chapter 7 Atomic Structure and Orbitals
Alpha Scattering Experiment: Rutherford s observations Light as Waves or Particles
Wavelength (λ) is the distance between any two identical points in consecutive cycles. Frequency (v) of a wave is the number of cycles of the wave that pass through a point in a unit of time. Unit = waves/s or s 1 (hertz). The relationship between wavelength and frequency: c = λv where c is the speed of light (3.00 x 10 8 m/s)
Planck: energy can only be absorbed or released from atoms in certain amounts called quanta. The relationship between energy and frequency is: E = hν where h is Planck s constant (6.626 10-34 J.s). To understand quantization consider walking up a ramp versus walking up stairs: For the ramp, there is a continuous change in height whereas up stairs there is a quantized change in height. The Photoelectric Effect and Photons Einstein assumed that light traveled in energy packets called photons. The energy of one photon: E = hν = hc/λ
The Bohr Model - Section 7.3
Line Spectra Radiation composed of only one wavelength is called monochromatic. Radiation that spans a whole array of different wavelengths is called continuous. White light can be separated into a continuous spectrum of colors. Note that there are no dark spots on the continuous spectrum that would correspond to different lines. Bohr Model Rutherford assumed the electrons orbited the nucleus analogous to planets around the sun. However, a charged particle moving in a circular path should lose energy. This means that the atom should be unstable according to Rutherford s theory. Bohr noted the line spectra of certain elements and assumed the electrons were confined to specific energy states. These were called orbits. Colors from excited gases arise because electrons move between energy states in the atom. ΔE = E f - E i = hν
Limitations of the Bohr Model Can only explain the line spectrum of hydrogen adequately. Electrons are not completely described as small particles. E n = -2.18 x 10-18 J(1/n 2 )
Knowing that light has a particle nature, it seems reasonable to ask if matter has a wave nature. Using Einstein s and Planck s equations, de Broglie showed: The momentum, mv, is a particle property, whereas λ is a wave property. de Broglie summarized the concepts of waves and particles, with noticeable effects if the objects are small. The Uncertainty Principle Heisenberg s Uncertainty Principle: on the mass scale of atomic particles, we cannot determine exactly the position, direction of motion, and speed simultaneously. For electrons: we cannot determine their momentum and position simultaneously. If Δx is the uncertainty in position and Δmv is the uncertainty in momentum, then Δx * Δmv > h/4π
Orbitals and Quantum Numbers If we solve the Schrödinger equation, we get wave functions and energies for the wave functions. We call wave functions orbitals. Schrödinger s equation requires 3 quantum numbers: 1. Principal Quantum Number, n. This is the same as Bohr s n. As n becomes larger, the atom becomes larger and the electron is further from the nucleus. 2. Azimuthal Quantum Number, l. This quantum number depends on the value of n. The values of l begin at 0 and increase to (n - 1). We usually use letters for l (s, p, d and f for l = 0, 1, 2, and 3). Usually we refer to the s, p, d and f-orbitals. 3. Magnetic Quantum Number, m l. This quantum number depends on l. The magnetic quantum number has integral values between -l and +l. Magnetic quantum numbers give the 3D orientation of each orbital.
Orbitals and Quantum Numbers Orbitals can be ranked in terms of energy to yield an Aufbau diagram. Note that the following Aufbau diagram is for a single electron system. As n increases, note that the spacing between energy levels becomes smaller. The s-orbitals All s-orbitals are spherical. As n increases, the s-orbitals get larger. As n increases, the number of nodes increase. A node is a region in space where the probability of finding an electron is zero. At a node, Ψ 2 = 0 For an s-orbital, the number of nodes is (n - 1).
The p-orbitals There are three p-orbitals p x, p y, and p z. The three p-orbitals lie along the x-, y- and z- axes of a Cartesian system. The letters correspond to allowed values of m l of -1, 0, and +1. The orbitals are dumbbell shaped. As n increases, the p-orbitals get larger. All p-orbitals have a node at the nucleus. The d and f-orbitals There are five d and seven f-orbitals. Three of the d-orbitals lie in a plane bisecting the x-, y- and z-axes. Two of the d-orbitals lie in a plane aligned along the x-, y- and z-axes. Four of the d-orbitals have four lobes each. One d-orbital has two lobes and a collar.