Chapter 7 The Quantum-Mechanical Model of the Atom (7.1-7.3) By Liad Elmelech (Mr. Elmelech)

The nature of Light Light has properties of both waves and particles Light is electromagnetic radiation Energy of fluctuating electric and magnetic fields Magnetic field - area were magnetic particles experience a force Electric field – are regions were electrically charged particles experience a force Travels at 3.00*10^8 m/s (on reference table)

Characterizing a wave Amplitude Height of crest or depth of trough Determines brightness Greater amplitude increases intensity Wavelength (λ) Length between crests Determines color of visible light Colors in order of increasing wavelengths Red, orange, yellow, green, blue, indigo, violet Frequency (v) Number of crests that pass through a point at in a given period of time Units: cycles per second (cycle/s or s^-1) Hertz(Hz) = 1 cycle/s

Equation for frequency and wavelength of light c = λv (on reference table) c is speed of light Calculate the wavelength, in nm, emitted by a barcode scanner that has a frequency of 4.62 * 10^14 s^-1. Nanometer = 10^-9 meters λ= c/v λ= (3.00*10^8m/s) / (4.62*10^14/s) λ= 6.49*10^-7m λ= 6.49*10^-7m * 1nm/10^-9m = 649nm

The electromagnetic spectrum In order of decreasing wave lengths / increasing frequency –radio, microwaves, infrared, visible light, ultraviolet, X-ray ,Gamma Ray Ultraviolet radiation, X-rays, and gamma rays can damage biological molecules http://www.ces.fau.edu/nasa/module-2/radiation-sun.php

Infrared radiation Associated with transitions in molecular vibrations Can be used to detect presence of different types of bonds Ultraviolet / visible radiation Associated with transitions in electronic energy levels Can be used to probe electronic structure

Interference Constructive interference When two waves of equal amplitude are in phase when they interact a wave with twice the amplitude results (in phase means that they align with overlapping crests) Destructive interference If two waves that are out of phase interact the waves cancel

Photoelectric effect Many metals emit electrons when light shines on them If frequency is too low than no electrons are emitted Einstein: “light energy must come in packets” E=hv (on reference table) E is the amount of energy in a light packet (also called a photon, or quantum) v is frequency h is the Plank’s constant 6.626*10^-34 Js (on reference table) v =λ/ c, therefore, E = hc / λ Diffraction Not purely a wave Light is a shower of particles

A nitrogen gas laser pulse with a wavelength of 337 nm contains 3 A nitrogen gas laser pulse with a wavelength of 337 nm contains 3.83 mJ of energy. How many photons does it contain? (number of photons = Epulse / Ephoton) λ= 337nm*(10^-9m/1nm) = 3.37*10^-7m E Photon = hc / λ = ((6.626*10^-34 J*s)(3.00*10^8 m/s)) / (3.37*10^-7m) =5.8985*10^-19 J 3.83 mJ *(10^-3 J / 1 mJ) = 3.83*10^-3 J Epulse / Ephoton = (3.83*10^-3) / (5.8985*10^-19) =6.49*10^15 photons

More about the photoelectric effect - Emissions of electrons from metal depends on whether a photon has enough energy to dislodge a single electron. This energy is ionization energy. Threshold frequency reached when energy of a photon (hv) = binding energy(φ) hv = φ Low frequency light does not eject electrons because no single photon has enough energy to dislodge Energy of a photon that is beyond what is needed to dislodge an electron is transferred to the electron in the form of kinetic energy KE = hv – φ Wave – particle duality of light Sometimes light behaves like a particle, at other times like a wave

Atomic Spectroscopy The study of electromagnetic radiation absorbed and emitted by atoms When an atom absorbs energy it often reemits that energy as light Different elements emit light of different colors Emission spectrum A series of lines created by passing light through a prism The emission spectrum of a particular atom is always the same Can be used to identify an element Niels Bohr attempted to create a model of the atom that explains the atomic spectra

The Bohr Model Electrons travel around the nucleus in circular orbits Exist only at fixed distances from the nucleus Fixed energy at each orbit (stationary state) Radiation is emitted or absorbed when electrons jump from one orbit to another The shorter jumps between stationary states produce light of lower energy Eventually replaced by the quantum – mechanical theory Do electrons in the current atomic model have fixed paths? No, they travel in there orbitals