Energy and Waves
1. In 1887 Hertz discovered the photoelectric effect, where electrons were emitted from a zinc surface when illuminated with ultra-violet light. These electrons (called ‘photoelectrons’) were only emitted when the frequency of the ultra-violet light was above a certain value (called the ‘threshold frequency’).
A. Assume that ultra-violet light is falling onto a piece of zinc, and photoelectrons are being emitted from the surface. As the intensity (brightness) of the ultra-violet light is increased, what happened to the kinetic energy of the photoelectrons?
If the intensity of the ultra-violet light is increased, more electrons will be emitted. There will be no change in the kinetic energy of the photoelectrons.
B. Explain why this discovery was not in agreement with the wave model of light.
According to electromagnetic theory, when light, thought to be composed of waves and falls on electrons bound in an atom, the energy of the liberated electrons ought to be proportional to the intensity of light. Experiments showed that, although the electron current produced depends upon the intensity of the light, the maximum energy of the electrons was not dependent on the intensity. Moreover, classical theory predicted that the photoelectric current should not depend on the frequency of the light and that there should be a time delay between the wave falling on the metal surface and the emission of the electrons.
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C. Describe the new photon model of light, which was proposed as a result of photoelectric effect.
In quantum theory light is composed of individual quanta or wave packets called photon. The energy of each photon being proportional to its frequency according to the equation E=hf, where E is the energy, (f) is the frequency, and (h) is Planck’s constant. Each photoelectron ejected is the result of the absorption of one photon. The maximum kinetic energy, KE, that any photoelectron can possess is given by hf= φ +KE, where φ is the work function, i.e., the energy required to free an electron from the material, varying with the particular material.
D. Calculate the energy of a photon of green light, whose frequency is 6 x 1014 Hertz.
E=hf f=6 x 1014 h= 6.6 x 10-34
E = (6.6×10-34) x (6 x 1014) = 3.9 x 10-19 Joule
E. In 1905 Einstein developed an equation that described the photoelectric effect. This equation is hf = φ + k.e. Explain what the following quantities represent?
(i) hf = energy of incident photon
h = planck’s constant
f = frequency of the photon.
(ii) Φ = work function
The work function is the minimum amount of energy required to remove an electron from the metal surface.
(iii) K.E = Kinetic energy of freed electron
2. An atom consists of a nucleus surrounded by electrons. A photon of light is emitted each time one of these electrons loses energy. The type and colour of light emitted depends on the amount of energy lost by the electron.
a. Explain the energy level model of the atom.
Quantum theory explains why atomic emission spectra consist of series sharp lines. Each line in an emission spectrum correspondent to an energy jump of a definite size as electrons drop back from a higher energy level to a lower energy level. The bigger the energy jump, the higher the frequency of electromagnetic radiation emitted.
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The energy gaps between energy levels get smaller as they get further from nucleus. As a result, in each series, the differences between the energy jumps get smaller.
B. Under what conditions will a photon of light be emitted?
Energy given to an atom excites an electron to an outer orbital, but the electron does not stay in the outer orbital. The electron prefers to be in lower energy level, so it de-excites back to its original orbital. In this process light (photon) is emitted.
C. The light emitted from a sodium discharge tube (like those found in street lights) can be passed through a prism, so what we can see all the colours emitted by the sodium atoms. Why is light of more than one colour emitted from single sodium atom? Use a diagram to help illustrate your answer.
The energy levels in atoms and ions are the key to the production and detection of light. Energy levels or “shells” exist for electrons in atoms and molecules. The different colours emitted from a single sodium atom are a result from electrons jump between these shells and each shell has its own characteristic energy level and therefore it causes different colours.
D. A photon of red light is emitted from a sodium atom, whose frequency is 5 x 1014 Hz. Calculate the amount of energy lost by a sodium electron, so that this photon can be emitted.
E = hf f = 5 x 1014 h = 6.6 x 10-34
E = (5 x 1014) x (6.6 x 10-34) = 3.3 x 10-19
