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Discover the wave nature of matter, electromagnetic radiation, and energy transfer through space. Understand wave characteristics like wavelength and frequency, Planck's constant, particle properties of energy, emission spectrum, and solve practice problems.
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Atomic Structure The wave nature of matter
Electromagnetic radiation • One of the ways that energy travels through space is by electromagnetic radiation. • Examples of electromagnetic radiation include: visible light, microwaves, radiant heat, X-rays, etc. • All of these forms of energy exhibit the same type of wavelike behavior and travel at the speed of light in a vacuum (3.0 x 108 m/s)
Wave Properties • Waves have three primary characteristics: wavelength frequency speed
Wavelength • The distance between two consecutive peaks or troughs in a wave • Symbol is λ • Measured in units of length; usually in nanometers (nm)
Frequency • The number of waves per second that pass a given point in space. • Symbol is ν • Measured in units of hertz (Hz) or cycles per second
Relationship between wavelength and frequency • As wavelength increases, frequency decreases. • λν = c
Practice Problem • What is the frequency of red light of wavelength 650 nm? • 4.6 x 1014 Hz
Planck’s Constant • While studying radiation given off by bodies exposed to incandescence, he discovered that only certain amounts of energy could be emitted. • Found that the energy emitted were in whole number multiples of a constant equal to 6.626 x 10-34 J (Planck’s constant) ΔE = nhν (n is an integer, h is Planck’s constant, and ν is the frequency of the energy emitted). • These discrete amounts of energy are referred to as a quantum of energy. • Sometimes referred to as the dual nature of light.
Particle Properties of Energy • Due to Planck’s discovery, Einstein proposed that electromagnetic radiation could be viewed as a stream of particles called photons. • Ephoton = hc/λ = h ν • In a related development, he derived the famous equation, E = mc2
Practice Problem • When CuCl is heated to 1200oC, a blue light having a wavelength of 450 nm is emitted. How much energy is emitted? • 4.41 x 10-19 J
DeBroglie’s Equation • This equation is based on the dual nature of light and allows us to calculate the wavelength for a particle. • λ = h/mv • λ is wavelength, m is mass in kg, v is velocity in m/s, and h is Planck’s constant (6.626 x 10-34 J . s or kg . m2/s ) • See problem 7.3 on page 281
Emission Spectrum • Electrons occupy the lowest energy state possible called the ground state. • If exposed to an outside energy source, electrons absorb energy and move to a higher energy state called the excited state. • Electrons give off this energy as they return to their ground state. • Because each atom has a unique arrangement of electrons, a characteristic emission spectrum is produced by each atom. • The energy absorbed or emitted can be calculated by the following equation: ΔE = -2.178 x 10-18 J ( 1/nfinal2 – 1/ninitial2)
Practice Problem • Calculate the energy required to excite the hydrogen electron from level n=1 to level n=2. • 1.633 x 10-18 J
Practice Problem • Calculate the wavelength of light that must be absorbed by a hydrogen atom in its ground state to reach this excited state. • 1.216 x 10-7 m