Photoelectric Effect and Quantised Radiation

The photoelectric effect

This is an additional dotpoint providing an overview of the photoelectric effect.

The photoelectric effect occurs when electromagnetic radiation (such as UV light) is shone on the surface of a metal. Photons are absorbed by electrons in the metal, which causes the electrons to be physically ejected from the surface of the metal. The velocity with which the electrons are ejected is dependent on the frequency of the radiation, while the quantity of electrons ejected depends on the intensity of the light.

The frequency of light at which the photoelectric effect commences is called the ‘threshold frequency’. Below this frequency, no electrons are emitted from the metal. The threshold frequency depends on the particular metal involved. The energy of the photon with a frequency equal to the threshold frequency is the ‘work function’ i.e. the work function is the value of E for E=hf_threshold.

Outline qualitatively Hertz’s experiments in measuring the speed of radio waves and how they relate to light waves

Make sure you can clearly describe how Hertz measured the speed of radio waves. It’s a popular exam question that people often find difficult to answer properly. It may help to read through dotpoint

  • first, for a description of the apparatus Hertz

 

Hertz was able to conclude that the radiation he was dealing with was part of the electromagnetic spectrum by analysing its properties in comparison to light. He carried out experiments to show that

  • It could be reflected by metal plates
  • It could be refracted by pitch or asphalt blocks
  • It could be diffracted around obstructions
  • It could be polarised (when he rotated the receiving coil he found that the sparks were stronger at certain angles compared to others)

And most importantly, that it travelled at the speed of light. Hertz connected the two loops together with a wire, so that there was interference between the AC wave in the wire and the wave caused by EMR transmission. From this, he was able to calculate the wavelength of the radio waves, and knowing the frequency of his wave generator he was able to show that the radio waves travelled at the speed of light.

Describe Hertz’s observation of the effect of a radio wave on a receiver and the photoelectric effect he produced but failed to investigate

Hertz discovered in 1887 that radio waves are capable of inducing currents in a receiver. In his experiment, he had a spark gap with a parabolic reflector connected to an induction coil that was constantly producing high voltage AC power and so constantly causing the spark gap to spark. A wire ring with a gap similar or identical to the spark gap in the transmitter was capable of receiving the radio waves, converting them to a spark between the gap in the receiver. This was clear proof that transmission and reception were occurring because there was no other source of electricity to the receiver to cause the spark. So Hertz observed that radio waves could induce currents in a receiver.

When he tried to enclose the receiver in a dark box to see the spark more clearly, the spark greatly diminished in size. Hertz concluded this was because light or more specifically, EMR, was affecting the size of the induced spark, and by irradiating the receiver with different frequencies of EMR he found that UV light maximised this effect. This was because of the photoelectric effect knocking electrons from the surface of the wire making it easier for them to jump the gap, although Hertz did not investigate this.

Wilhelm Hallwachs subsequently carried out experiments in which he shone different frequencies of EMR onto gold-leaf electroscopes to investigate the effect. A negatively charged electroscope would discharge in the presence of UV light while a positively charged electroscope would not. This was further evidence for the photoelectric effect, although it did not provide an explanation.

Remember- Hertz used rings with spark gaps to demonstrate induction, and found the effect was amplified when UV light was shone on the receiving ring. However, he never investigated this effect.

Identify Planck’s hypothesis that radiation emitted and absorbed by the walls of a black body cavity is quantised

Classical theory predicted that the radiation emitted by a black body should continuously increase in intensity as the wavelength became shorter, forming a continuous spectrum with intensities effectively corresponding to an exponential curve. This was not supported by experimental data which showed that the amount of energy radiated reaches a maximum at a wavelength that depends on the temperature of the black body, and then drops sharply for smaller wavelengths. Also, an exponential curve would violate conservation of energy since the total energy (the area under the graph) would be infinite. Planck resolved this problem with his hypothesis of quantised radiation which explained the experimental data, stating that radiation could only occur in small packets which he called “quanta”. The energy contained within a single quanta is dependent only on the frequency of the radiation according to the formula E = hf . Further, the vibration states of atoms in the black body cavity were also quantised, meaning that they could only have specific discrete frequency values. Since energy is only emitted when these atoms change vibrational states moving to a less energetic state, the energy released is also quantised.

Remember- Planck devised a theory to explain black body radiation, in which light was not considered a wave but as packets of energy that occurred only in multiples of a particular value.

Identify Einstein’s contribution to quantum theory and its relation to black body radiation

Einstein’s contribution was twofold. Firstly, he used Planck’s formula to create a more detailed quantum theory of light (with light packets called “photons”), and secondly he created an explanation for the photoelectric effect. In terms of defining light, he set up a concrete explanation for the particle theory, explaining intensity and frequency in terms of energy of and quantity of photons. He also stated that photons were the smallest units of light possible. In terms of its relation to black body radiation, Einstein’s theories came about directly because of the work undertaken by Planck regarding black bodies. Einstein’s work led him to explain the photoelectric effect in terms of work function and threshold frequency, also providing an explanation for photoelectron kinetic energy that matched Lenard’s puzzling results. Further, Einstein brought quantum theory further into the mainstream where other scientists continued to build on it.

Remember- Einstein applied Planck’s theories to black body radiation to produce a comparatively more detailed model of light as a particle, which served to bring quantum theory closer to mainstream science.

Identify data sources, gather, process and analyse information and use available evidence to assess Einstein’s contribution to quantum theory and its relation to black body radiation

The focus of this dotpoint is not so much on what the contribution was, but how valuable it was to science. As such, when answering this dotpoint bear in mind that you need to make a conclusion as to the value of Einstein’s contribution.

Einstein made a very significant contribution to quantum theory by taking Planck’s theories about black body radiation and applying them to solve a separate problem. Further, he expanded on the work of Planck and turned quantum theory into a set of ideas with concrete principles and modelling. Effectively, he took it seriously while Planck simply deemed it a mathematical trick. By using quantum theory to explain the photoelectric effect, solving a real problem with a concrete model for the solution that fully explained experimental observations, Einstein validated quantum theory, endorsed its solving of black body radiation, and opened the door for further research based on quantum ideas. Therefore Einstein made a significant contribution to quantum theory and its relation to black body radiation.

Remember- Einstein contributed significantly to quantum theory by applying Planck’s black body radiation theory to the photoelectric effect, thereby solving a real world problem.

Explain the particle model of light in terms of photons with particular energy and frequency

The particle model of light considers light to be transmitted by small particles. These particles have mass that depends on their energy, with more energetic photons having greater mass (although their rest mass is 0). To increase the energy of a photon, the frequency, not the amplitude of the light is increased. To increase the amplitude the number of photons is increased. Photon energies can only occur in multiples of Planck’s constant.

figure 7

Remember- Under the particle model, light exists as particles. More particles means greater intensity, and more energetic particles means higher frequency light.

Identify the relationships between photon energy, frequency, speed of light and wavelength

According to E = hf and c = , the relationships between variables can be deduced. Since the speed of light is constant, if the frequency of the light increases then wavelength decreases and vice versa. With photon energy, h is constant, so when f is increased photon energy increases (E is directly proportional to f ). Therefore it is inversely proportional to the wavelength λ, as deduced from the relationship between wavelength and frequency.

Identify data sources, gather, process and present information to summarise the use of the photoelectric effect in solar cells and photocells

Essentially, a solar cell consists of a junction between a P-type and N-type semiconductor that is exposed to light. Electrons are ejected from the N layer due to the photoelectric effect, and they then travel around a circuit to reach the P layer. This movement of electrons results in a potential difference that can be used to do work. In a photocell, the resistance of a circuit changes depending on how much light is falling on a semiconductor. Essentially, by monitoring voltage, current flow and resistance, a quantifiable measurement of light is possible because these properties change when a semiconductor experiences the photoelectric effect.

Remember- In solar cells the photoelectric effect is used to push electrons around a circuit, while in photocells it is used to measure light intensity.

Process information to discuss Einstein and Planck’s differing views about whether science research is removed from social and political forces

Einstein and Planck initially held differing views as to the relationship between science and politics, but in the end they both came to realise the two were intrinsically linked.

Einstein at first refused to support the war or use science to help governments fight the war, believing that science was removed from social and political forces. However, in the end he came to the realisation that the two are in fact linked together, and he ended up helping with the Manhattan project which almost certainly contributed to the ending of the war.

Planck initially felt that science definitely had a role to play in terms of politics, but eventually he turned against the Nazi regime, criticising it, believing that science should be separate. However, he understood that there is an unavoidable link between science and politics. Even after Planck attempted to separate science from politics, research science for the military continued through other scientists.

In a way, both Planck and Einstein are representative of the wider debate in science that continues even today as to the role the government’s agenda should be in terms of scientific research, but they, like today’s scientists, realised that science and politics can never be separated, even if that is the ideal situation.

Remember- Both scientists eventually agreed that science and politics are inextricably linked. They also agreed that ideally they would be separate. Einstein initially believed they had to be kept separate but then realised they couldn’t. Planck initially believed they had to be kept together, but then realised they shouldn’t.