to Atomic and Nuclear Physics to Atomic and Nuclear Physics Phil Lightfoot, E47, (24533) All these slide presentations are at: and also on FY website

Most Important Thing !!!!!! I’m always available to help with any aspect of the course Stop me if you’re confused My contact details are on the top of your lecture notes

Review of Electron-Volts This is such a tiny topic but it is also one of the most important ones. You will use electron-volts in two main ways; (i) as a convenient unit of energy, and (ii) to calculate the velocity of a charged particle passing through an electric field. Definition: The change in energy of a charged particle q as it moves through a potential difference V is given by : 1 electron-volt =1eV =1.6   1 = 1.6  J. In particle physics we often deal with very small energies and it is often therefore more convenient to refer to 3.2  J as 2 eV for example. Question : What is 11.2 × joules in electron-volts ? 1 electron-volt =1eV =1.6   1 = 1.6  J. Question : What is 12eV in joules ?

So what happened next in the history of particle physics ? Scientists investigate the things that are the most obvious first !!! In the history of particle physics scientists first wanted to know what the colourful discharges made by high electric fields in low pressure gas were. In 1896 Thomson investigated these effects and discovered the electron. He was also able to calculate the charge to mass ratio of the electron. Later in 1909 Millikan investigated the kinematics of charged oil vapour, and managed to calculate the charge of the electron. From this using Thomson’s charge to mass ratio, the mass of the electron could be found. So what happened next ?? Scientists didn’t just go looking for protons and neutrons guessing that they might be out there somewhere !!!!!! Instead they started looking at other puzzles and mysteries surrounding the atom…..

The Photoelectric effect background One of the biggest came to be known as the Photoelectric effect ….let’s look at a bit of background first….. Everyone knows that white light is made up of a spectrum of colours and that it can be split by transparent objects with high refractive indices like water or glass.

The Photoelectric effect background Light forms part of the electromagnetic spectrum and we can refer to the different colours in terms of either their wavelength nanometres or their frequency.

The Photoelectric effect background All members of the electromagnetic spectrum including radio waves, microwaves, X- rays, gamma rays, all travel at the speed of light (c = 3 × 10 8 ms -1 ) and all obey the relationship …. Where c is the speed of light in metres per second, f is the frequency of light in Hertz, and λ is the wavelength in metres. Question : If red light has a wavelength of 800 nm what is its frequency ? Question : If blue light has a frequency of 7.5×10 14 Hz, what is its wavelength ?

The Photoelectric effect Scientist noted that when some metals were illuminated by a strong source of light, electrons were emitted from the surface of the metal with a certain kinetic energy. They called this the photoelectric effect and the electrons are called photoelectrons to show how were created (although they are no different from normal electrons). But the scientists were confused. The kinetic energy of the ejected photoelectrons was found to depend on the frequency of light and the type of metal used and not, as expected, on the brightness of the light source. Intuitively we imagine that increasing the intensity of the incident waves would cause the kinetic energy of the ejected photoelectrons to increase, in the same way that a large intensity water wave would impart more kinetic energy to pebbles on a beach. However although the intensity of the incident light had no effect on the kinetic energy of the ejected photoelectrons, greater kinetic energy could be imparted to the ejected photoelectrons by increasing the frequency of the incident light!!! This whole thing came as quite a surprise, and more surprises were to follow !!!!!!

The Photoelectric effect This initially made no sense. The figure below shows the results observed.

Scientists at the time had no problem thinking of light as a wave. After all it didn’t seem to have any weight and it diffracted and reflected and transferred energy just like a water wave. The Photoelectric effect Finally Einstein offered an explanation in 1905 by proposing that light was not simply a wave but rather made up of tiny quanta or packets of energy, the energy of a single photon proportional to the frequency of light. They had a big problem thinking of it as a particle like a ball since then it would have to have weight and processes like interference and diffraction couldn’t be explained. What Einstein was saying was that we should actually think of light as a bunch of tiny packets of energy each with a small amount of energy. He even went further and said that each photon (packet of energy) would have an energy of : Where f is the frequency of the light and h is Plank’s constant (6.63 × Js)

Einstein proposed that there was a minimum energy E 0 required to release a photoelectron from a metal. The Photoelectric effect Where f is frequency of light and h is Plank’s constant (6.63 × Js), E 0 is the work function in joules. He called E 0 the work function and suggested that this value was a constant for a particular metal, but was different for different metals. When a photon is absorbed within a metal, some of the photon’s energy will be used up in freeing a photoelectron from the metal, and if there is any energy remaining, then this will appear as kinetic energy of the ejected photoelectron.

a) The fact that the number of photoelectrons increases with the intensity of the light is explained by each photon liberating exactly one photoelectron. A higher intensity of light implies that more photons are present and so more photoelectrons are ejected. The Photoelectric effect One photon ejects one electron More photons eject more electrons

b) The fact that the maximum kinetic energy of the photoelectrons depends on the frequency of light is explained because photons corresponding to light of a higher frequency carry more energy. So after E 0 has been used up, there is more energy left over to appear as kinetic energy of the photoelectron. The Photoelectric effect Where f is frequency of light and h is Plank’s constant (6.63 × Js), E 0 is the work function in joules. Since the frequency of yellow light is less than that of UV light, photons of yellow light have lower energy than UV photons. For the same metal, the kinetic energy of the ejected photoelectrons will be less for yellow light.

c) The fact that there is a lower limit for the frequency of light, below which no photoelectrons are emitted is due to the fact that since the minimum energy required to eject an electron is E 0, then the minimum frequency of light needed to do this is. The Photoelectric effect Where f is frequency of light and h is Plank’s constant (6.63 × Js), E 0 is the work function in joules. If then and no photoelectrons will be ejected. This will be true no matter how intense the light source is.

d) The fact that for the same light source some metals eject photoelectrons and other do not is due to the different work function E 0 of different metals. Metals, such as caesium, with a lower work function need less of the photon’s energy to release a photoelectron and so are more likely to exhibit photoelectron emission. The Photoelectric effect Where f is frequency of light and h is Plank’s constant (6.63 × Js), E 0 is the work function in joules. If the intensity and frequency of light is held constant, then the energy of a photon will simply be :. If the type of metal is changed then the work function will also change. This will result in a different E kinetic energy.

The Photoelectric effect Question : Imagine a ray of green light of wavelength λ = 530 nm incident on a metal with a work function of 1.1eV. What is the kinetic energy given to a photoelectron ejected from this metal? Tip: make sure that every value included is in the correct units. so and so To find frequency : To find single photon energy : To represent work function in joules : Answer : or

The Photoelectric effect Question : What is the lowest wavelength of light that can release an electron from a metal with a work function of 1.1 eV? Tip: make sure that every value included is in the correct units. Answer : Where f is frequency of light and h is Plank’s constant (6.63 × Js), E 0 is the work function in joules. But remember so and so Remember minimum energy means To represent work function in joules : and so so

More Questions on Photoelectric effect