Atomic Structure

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)

Emission Spectrum

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

Atomic Structure