Class notes for Chapter 2: Quantum-Mechanical Model in the class General Chemistry: Macroscopic Investigations and Reaction Principles (CHEM 130) at the University of Michigan. Subjects covered include wave natures of light and matter, electromagnetism, diffraction, the particle nature of light, Bo...
Schrodinger’s Cat
●Atoms/Particles are unimaginably small
○One speck of dust has more electrons than the number of people who have existed on Earth ever
●Quantum particles (such as electrons) can be in two different states at the same time ○An unobserved quantum atom can be both emitting a particle and not emitting a particle at the same time
■Act of observing/measuring the particle forces the atom into one state or the other
●Erwin Schrodinger: attempted to explain that quantum states can’t transfer to the macroscopic world with a thought experiment in which a cat is put into a chamber that has radioactive atoms. The chamber has a mechanism that, when an energetic particle is emitted by a radioactive atom, causes a hammer to break a flask that releases a poison and kills the cat.
○If the chamber is closed, the system is unobserved → radioactive atom is in a state in which it has emitted the particle and not emitted the particle with equal probability
■The cat is both dead and alive
○Demonstrated how quantum strangeness does not transfer to macroscopic world
●Quantum-Mechanic Model: a model that explains behavior of absolutely small particles
such as electrons and photons
The Nature of Light
●Light has many of the same characteristics as electrons
The Wave Nature of Light
●Electromagnetic Radiation: form of energy embodied in oscillating electric and magnetic fields
○Magnetic field: region of space where a magnetic particle experiences a force
○Electric field: region of space where an electrically charged particle experiences
a force
●We characterize waves by amplitude and wavelength
○Amplitude: vertical height of a crest of a wave
■Measure of wave intensity/brightness
■Greater amplitude → greater brightness
○Wavelength (λ - lambda): distance between adjacent crests of a wave
■Measured in units like meters or micrometers
■λ: Greek letter lambda
■Wavelength determines color ○Frequency ( - nu): 𝜈number of cycles that pass through a stationary point in a given period of time
■Units are cycles per second (cycle/s), s-1, or hertz (defined as 1 cycle/s)
■Directly proportional to the speed of the wave, inversely proportional to the wavelength
○Speed of light: C = 2.998 x 108 m/s = 𝜈λ
■C is the speed of light
■C and λ expressed in same unit of distance
○
●Visible Light: light that can be seen by the human eye
○Different colors = different wavelengths
○White light has a spectrum of colors
○Red light has the longest wavelength (750 nm), violet has the shortest (400 nm)
●When we see color, the object is absorbing every color except the one reflected back at our eyes
EX PROBLEM
What is the wavelength of a radio wave w frequency of 1.23 x 107 s-1?
Given: = 𝜈1.23 x 107 s-1
Find: λ
Strat: C = 𝜈λ → the units are (m)(1/s) → (m/s)
C = 𝜈λ → divide by 𝜈 on both sides → C/ 𝜈 = λ
Solve:λ = (2.998 x 108 m/s) / (1.23 x 107 / s) → s cancels out → 24.4 m
The Electromagnetic Spectrum
●Electromagnetic Spectrum: range of wavelengths of all possible electromagnetic radiation
○Main regions range from 10-15 m (gamma rays) to 105 m (radio waves)
■Visible light is only a small region in the middle ○
●Short-wavelength light inherently has greater energy than long-wavelength light
The Electromagnetic Spectrum (shortest to longest wavelength)
●Gamma Ray: form of electromagnetic radiation with the shortest wavelength and the highest energy
○Produced by the sun, stars, and some unstable atomic nuclei
○Excessive exposure is dangerous because they can damage biological molecules
●X-Rays: form of electromagnetic radiation with wavelengths slightly longer than gamma rays; used to image bones and internal organs
○Able to pass through many substances that block visible light
○Some annual exposure to X-rays is harmless but overexposure can increase risk of cancer
●Ultraviolet (UV) Radiation: electromagnetic radiation with slightly smaller wavelengths than visible light
○Component of sunlight that produces tan/burn
○Not as strong as gamma or X-rays but can damage biological molecules, increase risk of skin cancer, and cause premature wrinkling of the skin
●Visible Light: electromagnetic radiation with frequencies that can be detected by the human eye
○Does not have enough energy to damage biological molecules
○Causes certain molecules in our eyes to change shape and send a signal to our brains that lets us see it
●Infrared (IR) Radiation: electromagnetic radiation emitted from warm objects
○Invisible to our eyes but can be detected by infrared sensors
■Used in night vision technology to help people see in the dark
○We can feel it as heat
●Microwaves: electromagnetic radiation with wavelengths longer than IR radiation
○Used in radar and microwave ovens
○Lower energy than other lights but efficiently absorbed by water
■Can easily heat substances that contain water
●Radio Waves: form of electromagnetic radiation with the longest wavelengths and smallest amount of energy
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