Homework

# Physics 28: 1-6 The Wave Function and Uncertainty

## Homework

Text Reading: Giancoli, Physics - Principles with Applications, Chapter 28: 1-6.

##### Study Points
• 28: 1 Quantum mechanics allows us to use both wave and particle behavior concepts to explain our observations of atomic and macroscopic phenomena, including radiation and spectral behavior. At the macroscopic level, quantum mechanics predictions simplify to classical mechanics laws, showing that quantum mechanics corresponds to classical mechanics (the correspondence principle); it does not contradict classical mechanics where quantum effects are too small to be factors in behavior.
• 28: 2 In order to apply quantum mechanics to classical experiments with light, such as Young's double-slit experiment, we need to find corresponding applications for wave characteristics to particles. Per de Broglie's interpretation, wavelength maps to momentum of the particle. Electromagnetic (light) wave amplitudes are represented by fields E and B; matter wave amplitudes are represented by the Schrödinger wave function Ψ(position x, time t), which depends on the total energy of photons present. If this number is large, Ψ2 is proportional to the number of electrons found at the described point and time; if the number is small, Ψ2 gives the probability of finding the electron at (x, t).
• 28: 3The act of observing atomic particles affects the particle, since it may absorb or be changed during reflection of the light energy. This introduces a minimum uncertainty in all measurements.
• 28: 4 The Heisenberg uncertainty principle creates a philosophical or metaphysical challenge to the correspondence principle, since it runs counter to the deterministic basis of classical mechanics. In Bohr's Copenhagen interpretation, we must distinguish between our use of space and time "particle" descriptions of quantum objects under some circumstances, and the actual dual-nature of these particles.
• 28: 5 Rather than the planetary-orbit vision (Bohr's early model) of a discrete electron particle on a well-defined path, we must view electrons (and other quantum particles) as "clouds" with wave-like properties. We cannot pinpoint location, only probable existence within a given set of boundaries.
• 28: 6 To describe an electron orbital, we use four quantum numbers.
• Principle quantum number n, the energy level of the electron. This determines the distance of the orbital from the nucleus (1 is the lowest, closest possible level) Range: n = 1, 2, 3, ... ∞
• Orbital quantum number l, dependent on the angular momentum of the electron. This determines the shape of the orbital. Range: l = 0, ... (n-1). For example, if n = 3, l can take values 0, 1, and 2.
• Magnetic quantum number n, identifies the direction of the angular momentum. Determines the orientation of orbitals. Range: ml -l, ... 0, ... +l. For example, if l = 2, ml can take values -2, -1, 0, +1, and +2.
• Spin quantum number n, the direction of electron spin. Range: spin up (ms = +½), or spin down (ms = -½).

### Key Equations

PrincipleEquationVariables
Uncertainty (postion and momentum) Δx: Error in position
Δp: Error in momentum
h: Planck constant
Uncertainty (Energy and time) ΔE: uncertainty in energy
Δt: uncertainty in time
h: Planck constant
Energy for hydrogen electron at level n n: Energy level
E: energy of electron at level n
13.6eV: Base energy level (electron in 1st orbital)
Angular momentum of electron L: Actual Angular momentum
l: Angular momentum number, ranges 0 to n-1
Angular momentum direction/td>$L z = m l h 2 π$ Lz: Angular momentum along z axis
ml: magnetic quantum number for electron

### Web Lecture

Read the following weblecture before chat: Wave Functions and Uncertainty

### Study Activity

Use the Hydrogen atom simulator at the University of Nebraska-Lincoln to explore the hydrogen atom.

• Move the bar along the bottom grid to select a photon of a particular frequency, wavelength, or energy level. Start with eV = 0.03 (the minimum).
• Fire the photon. What happens?
• Set the photon to the first gride mark (0.97eV) and fire it. What happens?
• Select a preset value like the Lα wavelength (Lyman series) and fire the photon. What happens? [Lyman series photons affect electrons in the first energy level!]
• What happens if you fire a high energy photon at an already-excited electron?

### Chat Preparation Activities

• Forum question: The Moodle forum for the session will assign a specific study question for you to prepare for chat. You need to read this question and post your answer before chat starts for this session.
• Mastery Exercise: The Moodle Mastery exercise for the chapter will contain sections related to our chat topic. Try to complete these before the chat starts, so that you can ask questions.

### Chapter Quiz

• The chapter quiz is not yet due.

### Lab Work

If you want lab credit for this course, you must complete at least 12 labs (honors credit); you may complete more if you are preparing for the AP exam.. One or more lab exercises are posted for each chapter as part of the homework assignment. We will be reviewing lab work at regular intervals, so do not get behind!