Transcript Chapter 7
Chapter 6
Electronic Structure of Atoms
Lesson 1: The Wave Nature of Light
Much of our present understanding of our electronic structure of atoms has come from analysis o the light either emitted or absorbed by substances. To understand electronic structure of an atom, we must first learn about light .
Made up of
electromagnetic radiation
.
Waves of
electric and magnetic
fields at right angles to each other.
Parts of a wave
Wavelength – the distance between two adjacent peaks (or troughs) l Frequency = number of cycles in one second Measured in hertz 1 hertz = 1 cycle/second
= s -1
Frequency =
n
Kinds of EM waves
There are many different l
and
n Radio waves, microwaves, x rays and gamma rays are all examples.
Light is only the part our eyes can detect.
Gamma Rays Radio waves
Electromagnetic Spectrum
Wavelengths in the spectrum range from very short gamma rays to very long radio waves. Notice that the color of visible light can be expressed quantitatively by wavelength
The speed of light
in a vacuum is 2.998 x 10 8 m/s = c
c =
ln What is the wavelength of light with a frequency 5.89 x 10 5 Hz?
What is the frequency of blue light with a wavelength of 484 nm?
Sample Problems:
The yellow light given off by a sodium vapor lamp used for public lighting has a wavelength of 589 nm. What is the frequency of this radiation?
Sample Problem
A laser used in eye surgery to fuse detached retinas produces radiation with a wavelength of 640 nm. Calculate the frequency of this radiation.
Sample Problem
An FM radio station broadcasts electromagnetic radiation at a frequency of 103.4 MHz (megahertz = 10 6 s -1 ). Calculate the wavelength of this radiation.
6.15 a
What is the frequency of radiation that has a wavelength of 955 micrometers? (10 -6 meters)
6.15b
What is the wavelength of radiation that has a frequency of 5.50 x 10 14 s -1 ?
Lesson 2: Quantized Energy and Photons
Although the wave model of light explains many aspects of its behavior, there are several phenomena this model can’t explain.
Blackbody radiation – the emission of light from hot objects. Photoelectric effect – the emission of electrons from metal surfaces on which light shines.
Emission spectra – the emission of light from electronically excited gas atoms.
Hot Objects and the Quantization of Energy – Blackbody Radiation
Matter and energy were seen as different from each other in fundamental ways.
Matter was
particles
.
Energy could come in
waves
, with any frequency.
Max Planck found that as the cooling of hot objects couldn’t be explained by viewing energy as a wave.
Hot Objects and the Quantization of Energy
Planck found D
E
h n came in chunks with size D
E = nh
n where n is an integer.
and h is Planck’s constant h = 6.626 x 10 -34 J-s these packets of h n are called
quantum
The Photoelectric Effect - Einstein is next
Light shining on a clean metal surface causes the surface to emit electrons.
Said electromagnetic radiation is quantized in
particles called photons
.
Each photon has energy = h Combine this with E = mc 2 n = hc/ l You get the apparent mass of a photon.
m = h / (
l
c)
You Try It…
Calculate the energy of one photon of yellow light whose wavelength is 589 nm.
Sample Exercise
A laser emits light with a frequency of 4.69 x 10 14 s -1 . What is the energy of one photon of the radiation from this laser?
Sample exercise continued…
If the laser emits a pulse of energy containing 5.0 x 10 17 photons of this radiation, what is the total energy of that pulse?
Sample Exercise Continued
If the laser emits 1.3 x 10 -2 Joules of energy during a pulse, how many photons are emitted during the pulse?
Which is it?
Is energy a wave like light, or a particle?
Yes It is Both
Concept is called the
Wave -Particle duality
.
What about the other way, is matter a wave?
Yes
Lesson 3: Line Spectra and the Bohr Model (Emission Spectra)
The work of Planck and Einstein paved the way for understanding how electrons are arranged in atoms.
In 1913, the Danish physicist
Niels Bohr
offered a theoretical explanation of line spectra.
Additional Examples
Calculate the smallest increment of energy that can be emitted or absorbed at a wavelength of 438 nm.
Calculate the energy of a photon of frequency of 6.75 x 10 12 s -1 What wavelength of radiation has photons of energy 2.87 x 10 -18 Joules? In what portion of the electromagnetic spectrum would this radiation be found?
Another example
Molybdenum metal must absorb radiation with a minimum frequency of 1.09 x 10 15 s -1 before it can emit an electron from its surface via the photoelectric effect.
What is the minimum energy needed to produce this effect?
What wavelength radiation will provide a photon of this energy?
If molybdenum is irradiated with light of wavelength of 120 nm, what is the maximum possible kinetic energy of the emitted electrons?
Niels Bohr
Developed the quantum model of the hydrogen atom.
He said the atom was like a
solar system
.
The electrons were attracted to the nucleus because of opposite charges.
Didn’t fall in to the nucleus because it was moving around.
The Bohr Ring Atom
He didn’t know why but only certain energies were allowed.
He called these allowed energies
energy levels.
Putting Energy into the atom moved the electron
away
from the nucleus.
From
ground state to excited state.
When it returns to ground state it gives off
light
of a certain energy.
The Bohr Ring Atom
n = 4 n = 3 n = 2 n = 1
Give it some thought…
As the electron in a hydrogen atom jumps from n=3 orbit to the n=7 orbit, does it absorb energy or emit energy?
Line Spectra
A source of radiant energy may emit a single wavelength, as in the light from a laser.
This is known as monochromatic Most common radiation sources, including light bulbs and stars, produce radiation containing many different wavelengths.
When this radiation is separated into its different wavelength components, a spectrum is produced.
Continuous Spectrum vs. Line Spectrum
Continuous Spectrum
When a prism spreads light from a light bulb into its component wavelengths, a continuous spectrum is produced.
Most familiar example is the rainbow produced when raindrops or mist acts as a prism from sunlight.
Line Spectrum
Not all radiation sources produce a continuous spectrum.
When neon gas is placed under pressure in a tube and a high voltage is applied, the gas emits the familiar red orange glow of many “neon” signs.
When light coming from such tubes is passed through a prism, only a few wavelengths are present.
The colored lines are separated by black regions which correspond to wavelengths that are absent from the light.
A spectrum containing radiation of only specific wavelengths is called a
line spectrum
.
Sodium Line Spectrum
Flame Testing
Rydberg Equation
An equation that allows us to calculate the wavelengths of all the spectral lines present in a line spectrum.
Rydberg Equation
Lambda is the wavelength of a spectral line.
R H m -1 ) is the Rydberg constant (1.096776 x 10 7 n 1 and n 2 are positive integers, with n 2 being larger than n 1 . These will represent the energy level electrons reside in.
Energy levels
The lowest energy state (n=1) is the energy level
closest
to the nucleus. It can hold up to 2 electrons.
The next lowest energy state (n=2) is the energy level located outside energy level one, and so forth.
Ground State
– when the electron is found in its lowest energy level possible.
Excited State
– when the electron has absorbed energy to jump to an outer energy level.
Sample Exercise
Predict which of the following electronic transitions produces the spectral lines having the longest wavelength: n=2 to n=1 n=3 to n = 2 n=4 to n=3
Sample Exercise
Indicate whether each of the following electronic transitions emits energy or requires the absorption of energy A. n=3 to n=1 B. n=2 to n=4
Example Problem
For each of the following electronic transitions in the hydrogen atom, calculate the energy, frequency, and wavelength of the associated radiation, and determine whether the radiation is emitted or absorbed during the transition: From n=4 to n=1 From n=5 to n=2 From n=3 to n=6
Lesson 4: Matter as a Wave
Louis de Broglie proposed that the characteristic wavelength of the electron depends on its mass and on its velocity: Using the velocity v instead of the
frequency
n we get.
de Broglie’s equation l
= h/mv
Mass x velocity = momentum Note: mass must be expressed in Kg Can calculate the wavelength of an object.
The quantity mv for any object is called its momentum De Broglie used the term
matter waves
.
You Try It…
What is the wavelength of an electron moving with a speed of 5.97 x 10 6 m/s? The mass of an electron is 9.11 x 10 -28 g.
Example
Use the de Broglie relationship to determine the wavelengths of the following objects: An 85 kg person skiing at 50 km/hour A 10 gram bullet fired at 250 m/s A lithium atom moving at 2.5 x 10 5 m/s