Physics and the Quantum Mechanical Model

Light Electrons in atoms are arranged in orbitals, each with a particular energy level. When the electrons go to another energy level they either absorb or emit energy. Emitting energy produces light.

Light The quantum mechanical model grew out of the study of light. By 1900 light was known to consist of particles and waves.

Waves Each complete wave cycle starts at zero, increases to its highest value, passes through zero to reach its lowest value, and returns to zero again.

Waves The amplitude of a wave is the wave’s height from zero to the crest. The amplitude represents energy and is measured in meters.

Waves The wavelength, represented by lambda (λ), is the distance between the crests.

Waves The frequency is the number of wave cycles to pass a given point per unit of time. The frequency are usually cycles per second and is represented by the letter v. The SI unit of cycles per second is called a hertz (Hz).

Waves The speed of light is calculated by: C = λv The frequency and wavelength of light are inversely proportional to each other. As the wavelength of light increases, the frequency decreases.

Waves According to the wave model, light consists of electromagnetic (EM) waves. Electromagnetic radiation includes radio waves, microwaves, infrared waves, visible light, ultraviolet waves, x-rays, and gamma rays. All EM waves travel in a vacuum at a speed of 2.998 x 108 m/s.

Waves Sunlight consists of light with a continuous range of wavelengths and frequencies. The color of light found in sunlight depends on its frequency. When sunlight passes through a prism, the different frequencies separate into a spectrum of colors.

Waves A rainbow is an example of a spectrum each tiny droplet of water acts as a prism to produce a spectrum.

Waves In the visible spectrum (ROYGBIV), red light has the longest wavelength and the lowest frequency.

Calculating the Wavelength of Light Calculate the wavelength of the yellow light emitted by the sodium lamp if the frequency of the radiation is 5.10 x 1014 Hz. c = λv λ= c/v = (3.0 x 108 m/s) / (5.10 x 1014 Hz) Λ = 5.88 x 10-7 m/s

Calculating the Wavelength of Light 1. What is the wavelength of radiation with a frequency of 1.50 x 1013 Hz? Does this radiation have a longer or shorter wavelength than red light? 2. what frequency is radiation with a wavelength of 5.00 x 10-8 m? in what region of the EM spectrum is this radiation?

Atomic Spectra Atoms absorb energy that raises electrons into higher energy levels, and then lose the energy by emitting light when electrons return to lower energy levels.

Atomic Spectra Unlike sunlight, the light emitted by atoms consists of a mixture of only specific frequencies and is not a mixture of all visible frequencies. Each specific frequency of visible light emitted corresponds to a particular color.

Atomic Spectra When light passes through a prism the frequencies of light emitted by an element separate to give the atomic emission spectrum of the element. No two elements have the same emission spectrum.

Atomic Spectra Bohr’s model not only explained why the emission spectrum of hydrogen consists of specific frequencies of light. It also predicted specific values of these frequencies.

Atomic Spectra In the Bohr model, the lone electron in the hydrogen atom can have only certain specific energies. The lowest possible energy of the electron is its ground state.

Atomic Spectra In the ground state, the electron’s principal quantum number (n) is 1. Excitation of the electron by absorbing energy raises it from the ground state to an excited state with n = 2, 3, 4, 5, or 6 and so forth.

Atomic Spectra A quantum of energy in the form of light is emitted when the electron drops back to a lower energy level. This emission is called an electronic transition.

Atomic Spectra Bohr knew that this quantum of energy, E, is related to the frequency, v, of the emitted light by the equation: E = h x v H = 6.262 x 10-34J·s

Atomic Spectra The light emitted by an electronic transition from a higher to a lower energy level has a frequency directly proportional to the energy change of the electron.

Atomic Spectra Bohr’s theory of the atom was only partially right. It explained the emission spectrum of hydrogen but not the emission spectra of atoms with more than one electron. The quantum mechanical model replaced the Bohr model of the atom and is based on the description of the motion of material obejcts as waves.

Quantum Mechanics Einstein successfully explained experimental data by proposing that light could be described as quanta of energy that behave as if they were particles. Light quanta are called photons.

Quantum Mechanics Classical mechanics adequately describes the motions of bodies much larger than atoms, while quantum mechanics describes the motions of subatomic particles and atoms as waves.

Quantum Mechanics The Heisenberg uncertainty principle states that it is impossible to know exactly both the velocity and the position of a particles at the same time.