9.4.2-1(i) Hertz s first radio wave transmission demonstration Maxwell In 1865 James Clerk Maxwell predicted the existence of electromagnetic waves. He said that an accelerating charge would produce a wave made up of oscillating magnetic & Electric fields. He showed mathematically that the waves would propagate through space as a wave motion with a speed of 3 x 10 8 m/s. Heinrich Hertz, a German physicist, achieved the first experimental demonstration of EM waves in 1887. Hertz used an induction coil to produce oscillating electric sparks between two brass balls connected to two brass plates. The brass plates acted as an aerial system. He used a small loop of wire with a tiny gap in it as the receiver. The receiver was observed to have a spark whenever the induction coil was turned on indicating that an EM wave had traveled between the transmitter & receiver.
In Hertz s initial experiments he decided to place the receiver in a box to make it easier to see. To his amazement he quickly discovered that the sparks jumping the gap in the receiver were more vigorous when the receiver was exposed to the ultraviolet light coming from the sparks in the gap of the transmitter. (i.e. not in the box) He had just discovered what is now known as the photoelectric effect but he failed to investigate it further. When this was investigated further it offered results that conflicted with the classical theory of waves. 9.4.2-2(ii) Hertz s experiments on radio waves Once discovered these waves were thoroughly investigated by Hertz. He showed that they had properties similar to that of light. They showed :- - reflection - diffraction - refraction - polarization - interference One experiment had the EM waves reflecting off a sheet & interfering with each other. This produced a standing wave of which the wavelength could be calculated by measuring the distances between nodes. He then calculated the natural frequency of the radiation coming from the transmitter (irradiator) & then using v f he calculated the speed to be 3 x 10 8 m/s. Example: If a radio wave of frequency of 30000 khz was used in hertz experiment and the distance between nodes was measured at 5m, calculate the speed of the radio wave. Hertz s finding confirmed Maxwell s prediction & gave strong experimental support for the idea that light was a form of transverse EM wave. His experiment started the development of radio communications.
Problems with the classical wave theory of electromagnetic waves Towards the end of the 19 th century most of the behaviour exhibited by EM waves could be explained with the wave theory (i.e. reflection, refraction, dispersion, etc.). There were still a few experimental results that could not be explained by this theory. Two of these results were: - Black body radiation curves Photoelectric effect 9.4.2-2(iii) Black Body Radiation and Planck s hyptohesis When a black body is heated at different temperatures and the intensity (energy) of the EM waves emitted is plotted against their frequency an unexpected result is obtained. The black body used in these experiments was black cube with an internal cavity leading from a small hole in one side of the cube. The body was heated and the radiation that came from the body was measured from the small hole. This ensured that the light measured was coming intrinsically from the body and not reflected light. If the intensity at different frequencies coming from a heated black body was graphed it was found that the intensity peaked in the UV region and then abruptly fell to zero intensity. NB Hotter objects peak at higher frequency. According to the classical wave theory the graphs should not peak. They should continue to rise to the left indicating that most of the energy radiated by a hot object would be in the U.V./x-ray region. This became known as the Ultraviolet catastrophe. The current theory at the time could not agree with the experimental results. The lack of agreement outlined above led Max Planck, in 1900, to come up with a revolutionary new theory that has been refined these days as QUANTUM physics. He suggested that radiation was emitted or absorbed by a black body in discrete quanta (packets of energy) rather than continuously, as suggested by classical physics. He described this small, average packet as a quantum of energy. The energy of each quanta could be described by the following equation :- E hf where E = energy absorbed/radiated, h = Planck s constant = 6.6 x 10-34, f= frequency of the radiation absorbed/emitted.
By varying the value of the constant, h, he was able to match his theoretical curves with the experimental ones and from this was able to estimate what is now known as Planck s constant. More on the radiation of energy in quanta A quantum of energy (quanta for plural) is the smallest amount of energy that is able to be radiated from a body or absorbed by a body. An atom cannot radiate or absorb ½, ¼, 1 ½, etc of a quantum of energy it can only radiate/absorb whole number multiples of this basic minimum value. 9.4.2-(iv) The Photoelectric Effect and Einstein s contribution to Quantum theory In 1900, Philipp Lenard showed that the photoelectric effect (STUMBLED UPON BY Hertz) is actually the emission of electrons from the surface of material when the material is illuminated by light of high frequency. His apparatus is shown to the right. It consisted of light of different frequencies hitting a metal surface of one electrode in an evacuated glass tube. Electrons were ejected from the electrode and headed towards the other electrode At this point a current (photocurrent) was detected. He then applied a reverse voltage to stop these electrons reaching the other electrode. This magnitude of this voltage could be used to determine the kinetic energy of the ejected electrons (photoelectrons). He investigated how the kinetic energy of photoelectrons were related to the intensity of the light and the frequency of the light.
In these experiments Lenard found that: The number of electrons released (the photocurrent) is proportional to the light intensity. The emission of photoelectrons was virtually instantaneous (if it occurred). Emission was frequency dependent. There is a certain threshold frequency below which no photoelectrons were emitted. As the intensity of the light increased, the maximum kinetic energy of emitted electrons remained constant. As the frequency of light was increased, the maximum kinetic energy of emitted electrons also increased. ie the kinetic energy of photoelectrons was found to depend on the frequency of the light. The last four points could not be explained by the classical wave theory Einstein s explanation of the photoelectric effect The photoelectric effect results remained a mystery until Einstein wrote his Nobel Prize winning paper in 1905 (prize was awarded in 1921) which explained the photoelectric effect. That same year, which has been called Einstein's annus mirabilis, he published three other groundbreaking papers, including ones on special relativity and the equivalence of mass and energy*, which were to bring him to the notice of the academic world. He was 26 years old. *These two papers are covered in other areas of the HSC course. An outline of his explanation is outlined below. When a photon of light is strikes a metal surface it s energy (hf) is absorbed by the electrons of the metal. If this energy is enough the electron will be emitted from the metal. The conservation of energy holds in this interaction such that :- E MAX hf hf K where 0 where E K max = Maximum kinetic energy of electrons, h= Planck s constant, f= frequency of photon, work function, f 0 = threshold frequency. He explained that for an electron to be emitted a certain amount of work needed to be done (work function) & to do this the incident photon required a threshold frequency or higher. Both & f 0 were dependent on the type of metal since different metals have differing holds on their outer electrons.
Using Planck s hypothesis as a basis Einstein was able to explain all of the results observed in the photoelectric effect. This gave further support to Planck s hypothesis (ideas) on black body radiation. Debate still continues as to whom quantum theory should be credited as many believe that although being first to postulate the idea, Planck was probably only doing this to answer a specific problem rather than realising its wider implications. 9.4.2-2(v) Particle Theory of Light (The quantum nature of light) As well as explaining the photoelectric effect results, Einstein s 1905 paper also outlined the quanta nature of light. This was the beginning of what the syllabus refers to this as the particle theory of light. It states that light travels in packets of energy called photons rather than a continuous wave. Each photon has a specific amount of energy as described in the following equation:- E hf where E = energy absorbed/radiated, h = Planck s constant = 6.6 x 10-34 Js -1 f= frequency of photon (Hz) The wave equation still holds true as it did with classical wave theory. i.e. c f where c = speed of light (ms -1 ) f = frequency of light (Hz) = wavelength of light (m) Ex. Calculate the energy in one photon from a laser with a wavelength of 680 nm.
All photons of EMR travel at the same speed = 3 x 10 8 ms -1 Colour of light Wavelength (nm) Frequency (Hz) Energy (J) Number of photons in 1 J of energy* Number of photons/second in a 1 W light source RED 700 ORANGE 605 YELLOW 580 GREEN 540 BLUE 470 INDIGO 440 VIOLET 400 * Number of photons in 1J= 1/energy in one photon ** 1 W = 1J/s same answer previous column c f and we get Combining some students find it useful to remember this equation but it is not in the equation sheet.