One Chapter 9

The Franck - Hertz Experiment

• All of what we have said is building up evidence to support the Bohr model of the atom
  • We have seen that the Bohr model explains the fact that atoms absorb and emit the same frequencies of light
• There is another piece of evidence to support this view. It is the Franck - Hertz experiment.
• Franck and Hertz devised an experiment to investigate how atoms absorb energy in collisions with fast moving electrons
• They used this apparatus

• Electrons bubble off of the cathode and are accelerated to the screen. Most go through the screen and are collected on the anode. The micro ammeter measures the current and therefore the number of electrons collected on the anode.
• The experiment consists of increasing the accelerating voltage and measuring the current passing through the mercury vapour.
• The results are:
  • As accelerating voltage increases so is the current increased
  • At a potential difference of 4.9 V, the current drops
  • As voltage increases above 4.9 V, the current again increases
  • Minor decreases in current occur at 6.7 V and 8.8 V
  • Another significant decrease in current occurs at 9.8 V.
• Hertz found that for certain values of bombarding electron energy, the electrons do not easily make it through the mercury vapour
  • The reason for this is because electrons lose energy to the mercury atoms due to collisions only when the electrons have the correct energy to be absorbed
  • From 0 to 4.9 eV of energy for electrons, the collisions are elastic, and because the mass of the electron is much less than the mass of the mercury atoms, the electrons lose very little kinetic energy.
  • At 4.9 eV, the electrons lose all their kinetic energy when in collision with the mercury atoms, and therefore are drawn to the screen instead of passing through to the anode.
  • When the kinetic energy is greater than 4.9 eV, electrons collide with the mercury atoms and give up 4.9 eV in collision and retain the remaining energy. Therefore, they again reach the anode instead of the screen.
  • When the kinetic energy equals 6.7 eV and 8.8 eV, electrons again lose all their kinetic energy to the mercury atoms, but the collisions are less likely then at 4.9 eV. Therefore, the drop in current is less severe.
  • At a kinetic energy of 9.8 eV, an electron is able to make a collision and lose 4.9 eCV. This leaves 4.9 eV left over. The electron then makes a second collision with another mercury atom to lose the remaining 4.9 eV. This therefore produces the significant decrease in current at
  • 9.8 V
• Electrons colliding with an atom is like a marble colliding with a bowling ball. There should be little energy transfered.
• The Franck - Hertz experiment shows this is not true.
• At certain kinetic energies, large amounts of kinetic energy are lost. Therefore, this loss must not be to the nucleus, but to the electrons in orbit about the nucleus
• These losses are only certain amounts. Therefore, the electrons in the atoms must be able to absorb only certain energies.
• A mercury atom with electrons in ground state can absorb 4.9 eV as the smallest amount of energy it can absorb. When absorbed, this 4.9 eV would raise the mercury atom to its first excitation state.
• For mercury, 4.9 eV is the first excitation energy
• First excitation energy - the minimum amount of energy an atom can absorb to raise it from ground state to first excitation state.
• Energy levels - successive values of enternal energy that an atom can possess.

• For mercury atoms, 10.4 eV is the energy needed to strip electrons away from the atom
• When electrons are stripped away, they can carry any amount of energy with them.
• Ionization Energy - The amount of energy required to strip electrons from an atom.
• If the incident atoms have kinetic energy greater than 10.4 eV, then the electrons in the mercury atom can absorb any amount of this kinetic energy. What ever energy is not absorbed, remains with the incident electron as kinetic energy
• What we have said is true for any atom except
  • each type of atom has a different ioniation energy
  • each type of atom has a different set of energy levels

The Compton Effect

• The Hertz experiment varifified the existance of energy levels within the atom. This also varified the existance of stationary states as proposed by Bohr
• The Bohr model of the atom was necessary to explain the spectrum of atoms.
  • It was also necessary because atoms are the source of light, and we needed to explain particle like behaviour of light
  • The particle behaviour of light implies that light under the right circumstances, should show all the behaviours of particles. Therefore, light should carry momentum.
  • Comption was the first person to show that light carried momentum.
• Compton directed a beam of high energy X-rays with known frequency at a thin metal foil. This is similar to the photoelectric effect.
• Compton noted that not only electrons were emitted, but also low energy X-ray photons (Remember that E = hf, therefore lower frequency).
• COMPTON EFFECT - The scattering of lower frequency X-ray photons from a thin film.
• The presence of lower frequency X-rays regardless of the metal foil used, could not be explained by the electromagnetic wave theory.
• Compton suggested that the incident X-ray photons were behaving like particles. They encounter electrons, collide elastically, thereby losing some kinetic energy to the electrons.
• If these photons are behaving as particles, then the energy of the incident X-ray photon, must equal the energy of the scattered X-ray photon plus the energy of the emitted electron.

hf = hf^' + (1/2)mv²

• Similarly, the momentum of the incident photon, must equal the vector sum of the momentum of the scattered photon plus the momentum of the emitted electron.

Note that the following equation represents a vector sum.

P_(x-ray) = P^'_(x-ray) + P_(electron)

• P^'_(x-ray) represents the momentum of the x-ray after interaction.
• The question remains, what is the momentum of a photon? We can get a mass equivalent for a photon by using:

E = mc²

or m = E/c²

Therefore P = mv becomes

P = (E/c²)c = E/c

remember that E = hf = hc/l

Therefore P = (hc/l)/c

or P = h/l

• The last equation gives the momentum of a photon.
• Experimental results from Compton's experiments showed that energy is conserved as predicted. Results also showed that momentum was also conserved as predicted.
• The expression P = h/l , suggests that if a photon strikes a surface and is absorbed, then the surface must gain momentum so that momentum is conserved.
• Today we are able to measure the pressure of light on a surface. This confirms that the relationship P = h/l, is valid for the momentum of individual photons.
• From the photoelectric effect and the Compton effect, we see that five main interactions are possible. They are:
  • Simple reflection of the photon may occur.
  • A photon may liberate an electron and in the process disappear.
  • The photon may be scattered by an electron, and emerge with less energy and momentum.
  • A photon may interact with an individual atom, and in the process, elevate an electron to a higher energy level within the atom. The photon completely disappears. All of its energy has been given to the atom.
  • A photon can also disappear and create matter. This occurs in a process called PAIR PRODUCTION.
• An example of of pair production occurs when very high energy photon's collide with a heavy nucleus. The photon disappears and creates an electron and a positron. A positron has the same mass as an electron but with a positive charge.

January 22, 2014