Lecture Notes (Photoelectric Effect & X-Rays)

Intro: - in 1887 Heinrich Hertz discovered that light shone on a metallic object will cause the metal to emit electric charges; because both light and electricity were involved, it was called the photoelectric effect (PE)

- further study of these charged particles emitted by light, performed by J.J. Thomson in 1898, showed that they behaved just like cathode rays; therefore it was deduced that they were electrons (some people called them photoelectrons but they are still regular electrons) - the importance of the PE is seen in the development of the atomic theory; the effect could not be described in terms of classical physics - as a result, new ideas were formulated (quantum theory) to account for the experimental results Photoelectric Effect: - in 1905 Einstein published a paper in which he showed that radiant energy behaved not as an evenly distributed wave, but

rather as a series of particles called quanta (this led to a new branch of physics called quantum theory) - the PE shows that radiant energy in the form of x-rays, UV rays, or visible light hitting the surface of various metals ejects electrons from their surfaces - the PE was studied by making two kinds of measurements:

1) photoelectric current (electrons emitted per unit time) 2) KE of electrons after being emitted

- the device used to study the PE was similar to a cathode ray tube (two metal plates sealed in a vacuum tube made of quartz); the plates are connected by a wire to a voltage source and ammeter - quartz glass was used because it allowed visible and ultraviolet light to pass through to the metal plates

- depending upon the metal and the frequency of light used, electrons were emitted by the cathode and traveled to the anode, generating a current measured by the ammeter - the higher the frequency used, the greater the velocity and KE the ejected electron would have

- experiments showed that the frequency of light used had to be at a minimal level or higher to eject electrons from the surface of the cathode; (threshold frequency)

- this threshold frequency varied depending on what type of metal was used

- if electrons could be ejected from the cathode using a particular frequency, then experiments showed that the more intense the beam of light the more electrons were emitted (this generated a higher photoelectric current reading in the ammeter) - conversely, if the frequency of light used was not over the threshold frequency for the metal, no electrons would be ejected, no matter how intense the light source

- this was the first surprising discovery - the kinetic energy (KE) of the photoelectrons was studied by applying a repelling voltage; eventually a certain voltage is reached where no photoelectrons can reach the anode; as a result, the current becomes zero - this level of repelling voltage is called the stopping voltage, and is the measure of maximum (KEmax) of the emitted photoelectrons

KEmax = eVstop - where e is the charge of an electron

Photoelectricity Experimental Summary:

1) A metal shows a PE only if the incident light has a frequency above a certain threshold frequency (f0)

2) If light of a given frequency does produce a PE, the photoelectric current from the surface is proportional to the intensity of the light falling on it

3) If light of a given frequency releases photoelectrons, the emission of these electrons is immediate

4) The KE of the emitted electrons display a maximum value, which is proportional to the frequency of the incident light (above the threshold frequency)

5) The maximum KE of the photoelectrons increases in direct proportion to the frequency of the light that causes their emission. The max. KE is not dependant on the intensity of the incident light, as the classical wave theory of light would require.

- the question that stumped physicists was: How could a low- intensity train of light waves spread out over a large number of atoms, concentrate, in a very short time interval, enough energy on one electron to knock the electron out of the metal?

- according to classical wave theory, there was no reason why a high intensity beam of low frequency light should not produce photoelectricity if a low intensity beam of light at high frequency did - secondly, classical wave theory could not explain why higher frequency light ejected photoelectrons with more KE but the intensity light had no effect on KE Einstein's Theory of the PE: - Einstein won the Nobel Prize in physics in 1921 for his work on the PE - Einstein determined that light energy is not distributed evenly over the whole wave front but remains concentrated into lumps he called quanta - this energy is proportional to the frequency of the wave, but is independent of the amplitude (intensity); the proportionality factor is a constant called Planck's constant (symbol h)

E = hf - where h = 6.6 × 10-34 J/s

- Einstein said that the quanta (photons) have an energy equal to hf and eject the electrons of the metal; the quanta penetrate the metal & their energy is converted into the KE of the electron

- Einstein also said that the electron has to do work (symbol W) to leave the atom - the max. KE of an electron is:

KEmax = hf - W (Einstein's Photoelectric Equation) - if we include stopping voltage in the equation we get:

KEmax = hf - W = eVstop Millikan's Experimental Confirmation: - it wasn't until 10 years after his paper on photoelectricity, that the kinks had been worked out in experimentally verifying Einstein's photoelectric equation

- the difficulty was obtaining the W value for the metals used in the cathode; the impurities of the metals when exposed to the air were throwing off their results - this problem was solved by Robert Millikan in 1916; he developed an apparatus where the metal of the cathode was cut inside the vacuum tube itself

- this allowed for a pure metal surface, unaffected by impurities Applications of PE: - the PE is the basis of many modern day devices; for example, night vision goggles use the PE

Photons entering the device strike a plate which causes electrons to be emitted, these pass through a disk consisting of millions of channels, the current through these are amplified and directed towards a fluorescent screen which glows when electrons hit it.

Quanta: - although Einstein used the term quanta to describe the bundled units of light energy, he was not the first person to suggest this - rather, the idea that EM radiation was quantized first came from a German physicist named Max Planck

- Planck discussed this idea in 1900, five years prior to Einstein's paper on the PE - Planck came up with this idea while studying heat and light emitted by hot solids - Planck related the energy radiated by a hot solid to the frequency of the radiation given off - classical physics could not explain his experimental results; so Planck came up with his new idea that atoms radiate energy in bundles (quanta) - the amount of radiant energy in each lump is called a quantum of energy (now it is called a photon)

- Einstein's PE theory was actually an extension of Planck's work; Einstein said that the change in the atom's energy being carried off was located in a distinct photon of energy rather than being spread out continuously over the light wave

Shortest Wavelengths (Most energetic photons) Longest Wavelengths (Least energetic photons) PE Dilemma: - the PE presented physicists with a problem; according to classical wave theory, light consists of EM waves extending continuously throughout space - this worked well in explaining such wave characteristics as polarization, reflection, refraction, interference, and diffraction - Maxwell's ideas, however, could not explain the PE

- Einstein's theory said that light energy is bundled into discrete units now called photons; Einstein's theory worked to explain the PE, but could not explain interference of light - the result is two models of light whose basic ideas contradict one another; one says light behaves like a wave; the other said it acts like a particle X-Rays: - X-ray radiation was discovered in 1895 by a German physicist named Wilhelm Röntgen

- like the PE, it too did not fit with classical physics theories - it eventually required the idea of quanta to completely explain their effects - the discovery of X-rays, which were often called Röntgen rays, had important consequences for atomic physics, medicine, and technology - Röntgen discovered X-rays while experimenting with cathode ray tubes; he noticed that a screen coated with a fluorescent material (barium platinocyanide) glowed from something being emitted by the cathode ray tube

- barium platinocyanide was know to glow when exposed to UV radiation, but no UV light was coming from the cathode ray tube; Röntgen hypothesized that some new form of radiation was affecting the screen - he named them X-rays since they were of an unknown nature - experiments performed by Röntgen showed that X-rays originated from the glass wall of the cathode ray tube, they traveled in straight lines, darkened photographic plates, penetrated various substances and were not deflected my magnetic fields

- J.J. Thompson discovered that upon passing through a gas, X- rays electrify (ionize) the gas - there was some debate as to whether X-rays were particles or waves; because they were not effected by magnetic fields, they were thought to be either neutral particles or EM waves - if they were EM waves, scientists knew that they would have to have a very short wavelength

- to test their wave nature a diffraction grating with slits 10-10 m apart would have to be used; they used crystals in which the atoms were spaced about 10-10 m, instead of a diffraction grating

- the atoms in the crystal acted like a diffraction grating and an interference pattern was observed - the interference pattern, however, was in three dimensions instead of two dimensions seen in Thomas Young's experiment

- this 3-D image was more complicated to study, yet still effectively proved the wave nature of X-rays - after the discovery of X-rays, there was a great wave of excitement from the scientific and business community - hospitals used X-rays for medical tests, industry used X-rays for viewing the inner structure of materials; for example, engineers used X-rays to study welds and defects in structures)