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The Development of the Model of the Atom

 In the Thompson model of the atom all the mass and the entire positive charges where distributed evenly throughout the atom. The electrons where embedded in the atom like raisins in a pudding. J.J. Thompson discovered the electron and called his model of the atom a "plum pudding" model.  In this model the atom was a positive charged core (ball) in which negatively charged particles (electrons) were embedded like raisins in a pudding.

 J. J. Thompson model of the Atom

Mutual repulsion of the electrons separated them uniformly through the body of the atom.  The resulting association of positive and negative charges was reasonable and explained such properties an atomic neutrality and atomic ionization.

 Rutherford disproved the raisin pudding model when he performed the gold foil experiment.

 Rutherford’s model stated that there was an extremely dense, positively charged nucleus, in which all the mass is concentrated, surrounded by a region of negatively charged electrons.  The electrons are found in a region with a radius 100 000 x that of the nuclear radius.

 

The Rutherford atomic model has been alternatively called the nuclear atom, or the planetary model of the atom

         Probably the most serious problem with the planetary model is that an orbiting electron has a centripetal acceleration and (according to Maxwell's theory of electromagnetism) ought to lose energy by emitting electromagnetic radiation at a frequency equal to that of the orbital motion (the reciprocal of the orbital period). This radiated energy would be at the expense of the electrostatic potential energy of the electron, which would become more negative - implying that the electron approaches closer to the nucleus and experiences an increased electrostatic force. This increased force implies an increased centripetal acceleration and a higher angular velocity of the orbiting electron; the frequency of the emitted radiation would increase and the electron would spiral into the nucleus. Calculations showed that this process should happen in a small fraction of a second; in other words, the atom should not be stable !

            The realization that radio waves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays were all forms of ELECTROMAGNETIC WAVES with different wavelengths led to a further understanding of the atom.

These waves can be described by their wavelength, lambda, λ, amplitude and frequency, nu, υ .  Frequency is the number of cycles of a moving wave that pass a given point per unit time.

Units for frequency are given in cycles/second or Hertz (Hz)

The units for wavelength are in length, the common units being meters, nanometers and Ε, angstrom.

 

The relationship between wavelength and frequency is given by Maxwell’s equation

 c = λ υ

Sample problems:

1. Yellow light has a wavelength of 600 nm. What is its frequency?

Given: λ = 600 nm;      since 1 nm = 10-9 m;       then 600 nm = 6.00 x 10-7 m

          c = 3.00 x 108 m/s

Required:  find the frequency, υ, of yellow light

Analysis: since c = λ υ

               then  υ  =  c/λ

Solution: υ = 3.00 x 108 m/s χ 6.00 x 10-7 m

                  = 5.00 x 1014 cycles/s

Statement: The frequency of yellow light is 5.00X 1014 s-1

Complete the following questions.

  1. Radio station CFMY in Toronto, broadcasts at a frequency of 1021 kHz. What is the wavelength of these radio waves, expressed in meters? (242 m)
  2. A certain substance strongly absorbs infrared radiation having a wavelength of 6.50 ΅m.

What is the frequency in hertz of this light? (4.62 x 1013 Hz)

Waves in the electromagnetic spectrum vary in size from very long radio waves the size of buildings, to very short gamma-rays smaller than the size of the nucleus of an atom.

The electromagnetic spectrum includes, from longest wavelength to shortest: radio waves, microwaves, infrared, optical, ultraviolet, X-rays, and gamma-rays.

Radiation of different wavelengths affects matter differently, for example overexposure to infrared radiation causes a “heat burn”, overexposure to visible and near ultraviolet light causes sun burn and sun tan, while overexposure to X ray radiation causes tissue damage. These different effects are due to the ENERGY of the radiation.

Now electromagnetic waves can not only be described by their wavelength, but also by their energy and frequency? All three of these things are related to each other mathematically. This means that it is correct to talk about the energy of an X-ray or the wavelength of a microwave or the frequency of a radio wave.  Radiation of high frequencies and short wavelengths are more energetic than radiation of lower frequencies and longer wavelengths. The quantitative relationship between frequency and energy was developed by Max Plank.

By studying black body radiation Max Plank developed the rudiments of the quantum theory of matter.

What is a black body? A black body is a theoretical object that absorbs 100% of the radiation that hits it. Therefore it reflects no radiation and appears perfectly black. In practice no material has been found to absorb all incoming radiation, but carbon in its graphite form absorbs all but about 3%. It is also a perfect emitter of radiation. At a particular temperature the black body would emit the maximum amount of energy possible for that temperature. This value is known as the black body radiation. It would emit at every wavelength of light as it must be able to absorb every wavelength to be sure of absorbing all incoming radiation. The maximum wavelength emitted by a black body radiator is infinite. It also emits a definite amount of energy at each wavelength for a particular temperature, so standard black body radiation curves can be drawn for each temperature, showing the energy radiated at each wavelength.

BLACK BODY RADIATION CURVES

 

Fig 1: Theoretical black body curve for 5000K

The black body radiation curve (Fig1) shows that the black body does radiate energy at every wavelength. The curve gets infinitely close to the x-axis but never touches it. The curve touches at infinite wavelength. It also shows that the black body emits at a peak wavelength, at which most of the radiant energy is emitted. At 5000K the peak wavelength is about 5x10-7m (500nm) which is in the visible light region, in the yellow-green section. At each temperature the black body emits a standard amount of energy. This is represented by the area under the curve.
 
 

Fig 2: Black body radiation curves showing peak wavelengths at various temperatures

This graph shows how the black body radiation curves change at various temperatures. These all have their peak wavelengths in the infra-red part of the spectrum as they are at a lower temperature than the previous graph.
The graph shows:
1. As the temperature increases, the peak wavelength emitted by the black body decreases.

2. It therefore begins to move from the infra-red towards the visible part of the spectrum. Again, none of the graphs touch the x-axis so they emit at every wavelength. This means that some visible radiation is emitted even at these lower temperatures and at any temperature above absolute zero, a black body will emit some visible light.
The graph also shows:

3. As temperature increases, the total energy emitted increases, because the total area under the curve increases.

4. It also shows that the relationship is not linear as the area does not increase in even steps. The rate of increase of area and therefore energy increases as temperature increases.

The failure of physics to account for the decrease in energy emitted at short wavelengths (the ultraviolet wavelengths) became known as the ultraviolet catastrophe. A major breakthrough was made by Max Planck who made a formula that agreed with experimental data. However, he had major problems proving this law. His idea was that the oscillating electrons of the surface atoms of the black body emitted radiation according to Maxwell's laws of electromagnetism. Before Planck it was assumed that these could have any value of energy but Planck decided that the energy must go up in discrete amounts (quantized) because the frequencies of the oscillating electrons could only take certain values. As energy is proportional to frequency    E = hυ,

Where h is the Planck constant 6.626 x 10-34 Js

If frequency can only take discrete values, this means that energy is also quantized. The electrons have a fundamental frequency (like standing waves on a string) and the frequency can only go up in whole multiples of this frequency, called the quantum number. This assumption led Planck to correctly derive his formula.

 Einstein took the next step by working out that all radiation is quantized. He argued that an oscillating charge can accept or lose energy in small values of DE = hDυ. This energy is lost as electromagnetic radiation. Therefore this radiation must be emitted in small packets, each containing  DE. He then suggested that each energy of radiation will have its own frequency. Therefore he no longer thought of radiation from an object as continuous. He said it consisted of a series of "packets" of energy. This meant that radiation was being thought of as a "packet of energy" but also as a wave because it had a frequency. These became known as photons.

THE PHOTOELECTRIC EFFECT

  This is an effect that is best explained by Einstein's photon model of electromagnetic radiation. When light is shone on metal , the surface may become positively charged. This is because electrons gain energy from the light waves, and are able to leave the metal's surface. However, there were some strange effects that could not be explained by considering light as a wave. The frequency of the light must be above a certain threshold value for that metal for electrons to be emitted. For example blue light causes sodium to emit electrons but red light does not. If light was a wave the electrons would eventually absorb enough energy to be emitted, regardless of frequency. Also, incredibly weak beams of light can cause electrons to be emitted. If light was a wave and spread out you would not expect any electrons to obtain the energy to escape. Finally it was discovered that the kinetic energy of the electrons depends not on the intensity of the light but on its frequency. A very weak ultraviolet beam will give electrons a higher kinetic energy than a very bright blue beam of light. Einstein explained this by saying that the light arrived in photons. One photon gave all its energy to one electron. The electron must gain a certain amount of energy to overcome the forces that hold it inside the metal. It appears that one electron can only accept one photon of energy, so this must have the required frequency to have the necessary escape energy, so the intensity will not make any difference to this. Brighter light means there are more photons, so more electrons can be emitted, but it is the frequency of the light that decides the energy of the photon and so the electron's kinetic energy. Electrons can also be emitted very quickly because it only requires one photon for emission to occur, not the gradual build up of wave energy.

 

From the above we see that atoms absorb or emit light of certain frequencies. How can we relate frequency, energy and wavelength.

 λ and υ  are related by the equation                c = λ υ  ………………….Equation (1)

Energy of a photon is given by the equation      E = h υ  ……………………….. Equation (2)

Combine equations 1 And 2

                                           Since   υ = c/λ

                                            Then   E = h c/λ  …………………………………………………….Equation (3)

  Equation 3 can be expressed as   E = h c/λ   this equation is used to calculate the energy of a photon in transition.  E is a change in energy.