Although Planck's resolution of the "ultraviolet catastrophe" for the blackbody radiation spectrum assumed that electromagnetic radiation is quantized in packets of energy we call photons, it was not understood if this was reality, or simply a coincidence of nature. The photoelectric effect was the first clear demonstration that photons are real, not just a fudge.
The photoelectric effect occurs when light (visible or ultraviolet) shines on a metal. Energy from the light can cause electrons to be ejected from the surface of the metal. Let's review the reasons why the photoelectric effect supports the postulate of quantization of electromagnetic energy in photons.
The photoelectric effect experiments use a device called a photocell. A photocell is made of two "electrodes" (pieces of metal) inside of an evacuated glass bulb. (drawing like Figure 27.4) One of the electrodes is prepared for the photoelectric effect, and is called the photocathode (a cathode is a source of electrons). The second electrode doesn't participate in the photoelectric effect, but is intended to collect the ejected electrons, and is called the anode.
When light shines on the photocathode, electrons are ejected, and a current is produced. A potential can be applied between the electrodes to enhance or limit the current. The photocell acts like a switch that is turned on or off by light.
If light is a continuous wave instead of being quantized in photons, then how would we expect a photocell to behave.
The experiments observe different behavior.
Einstein is the one who explained the observations by suggesting that electromagnetic radiation is quantized in photons. According to Einstein, the energy of the photon, hf, is transferred to a single electron. There's a certain minimum amount of energy required for the electron to leave the surface of the metal, known as the work function, f. The resulting maximum kinetic energy of the electron is the difference between the photon energy and the work function:
If the frequency is less than the cutoff frequency, then hf < f, and there is not sufficient energy for the electron to be ejected from the metal. The cut off frequency is given by hfc = f. We can use the relation between frequency and wavelength to find the cutoff wavelength:
Consider the metals lithium, aluminum, and mercury, which have work functions of 2.3eV, 4.1eV, and 4.5eV, respectively. If light of wavelength 3.0×10-7m is incident on each of these metals, determine (a) which metals exhibit the photoelectric effect and (b) the maximum kinetic energy for the photoelectrons for those that exhibit the effect.
(a) Begin by calculating the energy in eV of photons of light of the given wavelength.
Eph = hf = hc/l = (6.63×10-34Js)(3.0×108m/s) / (3.0×10-7m)(1.6×10-19J/eV) = 4.1eV.
The photoelectric effect is exhibited when the photon energy is greater than the work function.
This is true for lithium (2.3eV), but not so for aluminum (4.1eV) and mercury (4.5eV).
(b) For lithium, KEmax = hf - f = 4.1eV - 2.3eV = 1.8eV.
There are many applications of the photoelectric effect. Most of them apply a photocell to a problem -- controlling street lights, the breathalyzer, and electric eyes. Many of these have replaced the photocell with the more modern, solid state photodiode. The device may have changed, but the idea is the same.
Many modern experiments use a variant of the photocell which is capable of detecting single photons, the photomultiplier tube. For instance, biological studies which rely on measuring the flouresence of a tracer molecule generally use photomultiplier tubes to measure the small number of flouresence photons.
In 1895, Wilhelm Roentgen discovered x-rays, thus marking the beginning of modern physics. X-rays are a form of electromagnetic radiation, like radio waves and light, but having higher frequency and energy than either. The energy of x-rays is higher than the electron binding energies of light atoms. This enables x-rays to easily pass through water and tissues, composed mostly of hydrogen, carbon, nitrogen, and oxygen, while they will tend to scatter off of bones with their high density of calcium.
When originally discovered, it wasn't clear what x-rays where, hence the reason behind the name. It was easily verified that x-rays are not deflected by electric or magnetic fields, and therefore are not charged particles.
It took a demonstration of diffraction of x-rays by a crystal, from which their wavelength could be calculated, and conclude that they are electromagnetic waves.
A common way to produce x-rays is to rapidly decelerate high energy electrons, for instance by having them hit a target made of heavy atoms. An x-ray tube is a device that does just this. The resulting x-rays have a broad spectrum of energies, plus some sharp lines corresponding to atomic energy levels of inner shell electrons.
The x-ray is created when the electron passes near the nucleus of an atom and feels its electric field.
This process is like a collision of billiard balls, or the inverse of the photoelectric effect.
The maximum x-ray energy, and minimum wavelength results when the electron loses all its energy in a single collision, such that
eDV = hfmax = hc/lmin
or therefore
What minimum accelerating voltage would be required to produce an x-ray with a wavelength of 0.0300nm?
Since lmin = hc/eDV, we can turn this around to find
DVmin = hc/el = (6.63×10-34Js)(3.0×108m/s)/(1.6×10-19C)(3.00×10-11m) = 4.1×104V = 41kV.