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### Chapter 5

Electrons in Atoms

Wave Nature of Light

- Electromagnetic radiation which is a form of energy that exhibits wavelike behavior as it travels through space.
- Examples: light, radio waves, x-rays, etc

Wavelength

- Waves have a repetitive nature.
- Wavelength- ( lambda)
- shortest distance between corresponding points on adjacent waves.
- Measured in units like meters, centimeters, or nanometers depending on the size.
- 1 x 10-9 meters = 1 nanometer

Frequency

- # of waves that pass a given point per second.
- Units are waves/sec, cycles/sec or Hertz (Hz)
- Abbreviated n the Greek letter nu or by an f
c = lf

Frequency and wavelength

- Are inversely related
- As one goes up the other goes down.

High frequency, Short Wavelength

Low frequency, Long Wavelength

Wave Formula

- All electromagnetic waves, including visible light, travel at the speed of 3.00 x 10 8 m/s in a vacuum.
- Speed of light = c = 3.00 x 108 m/s
c=f

Speed of light = (wavelength) x (frequency)

Example Problem

- What is the wavelength of a microwave having a frequency of 3.44 x 109 Hz?
Formula: c=f

- = ?
f = 3.44 x 109 Hz

c = 3.00 x 108 m/s

3.00 x 108 m/s = (3.44 x 109 s-1)

3.00E8 / 3.44E9 = 8.72 x 10-2 m

Practice

- What is the frequency of green light, which has a wavelength of 5.90 x 10-7m?
- A popular radio station broadcast with a frequency of 94.7MHz, what is the wavelength of the broadcast? ( frequency needs to be is Hz)

- Different frequencies produce different types of waves.
- The entire range of frequencies is called the electromagnetic spectrum
- We are only able to see with our eyes a small portion of the spectrum = visible light
- ROY G BIV
- Different colors mean different frequencies/wavelengths

Energy & The Spectrum

- The energy of a wave increases with increasing frequency
- High Frequency = High Energy
- Low Frequency = Low Energy
- Blue light has more energy than Red light

Low energy

Low Frequency

High Frequency

X-Rays

Radiowaves

Microwaves

Ultra-violet

GammaRays

Infrared .

Long Wavelength

Short Wavelength

Visible Light

Quanta

- Max Planck suggested the idea of quanta or packets of energy.
- Quanta is the minimum amount of energy that can be lost or gained by an atom.
- Energy is quantized = it comes in packets (like stairs or pennies only whole numbers)

Planck’s Constant

- h = 6.626 x 10-34 J.s (Joule seconds)
Energy = (Planck’s constant)(frequency)

E = hf

Example: What is the energy in Joules of a photon from the violet portion of the rainbow if it has a frequency of 7.23 x 1014 Hz?

E = ?

h = 6.626 x 10-34Js

f = 7.23 x 1014 Hz (or s-1)

E = (6.626 x 10-34Js)(7.23 x 1014 s-1)

E = 4.79 x 10-19 J

Photoelectric Effect

- In the 1900s, scientist studied interactions of light and matter.
- One experiment involved the photoelectric effect, which refers to the emission of electrons from a metal when light shines on the metal.
- This involved the frequency of the light. It was found that light was a form of energy that could knock an electron loose from a metal.

Photon

- Light waves can also be thought of as streams of particle.
- Einstein called these particles photons (He won a Nobel Prize for this)
- A photon is a particle of electromagnetic radiation having zero mass and carrying a quantum energy.

Bohr’s Model

- Why don’t electrons fall into nucleus?
- Bohr suggested that they move like planets around sun.
- Certain amounts of energy separate one level from another.

Bohr’s Model

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- Further away from nucleus means more energy.
- There is no “in between” energy
- Energy Levels

Fifth

Fourth

Third

Increasing energy

Second

First

Nucleus

Bohr Model of the Atom

- Ground state- the lowest energy state of an atom.
- Excited state – state in which an atom has a higher potential energy than its ground state.
- Energy is quantized. It comes in chunks.
- quanta - amount of energy needed to move from one energy level to another.
- Since energy of an atom is never “in between” there must be a quantum leap in energy.

Bohr Energy Levels

- K = 2 electrons – 1st
- L = 8 electrons – 2nd
- M = 18 electrons – 3rd
- N = 32 electrons – 4th

Heisenberg Uncertainty Principle

- This is the theory that states that it is impossible to determine simultaneously both the position and velocity of an electron or any other particle.

Quantum Theory

- Schrodinger derived an equation that described energy & position of electrons in atom
- Schrodinger along with other scientists laid the foundation for the modern quantum theory, which describes mathematically the wave properties of electrons and other very small particles.

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