More About Photoelectricity Quantum Physics Lesson 2

Learning Objectives Define the work function & threshold frequency State and use the photoelectric equation. Explain why electrons leave with a range of kinetic energies. Plot the results from the vacuum photocell to determine Planck’s constant and the work function.

THE ‘ULTRAVIOLET CATASTROPHE’ Rayleigh This was a CLASSICAL prediction, first made in the late 19th century, that an IDEAL BLACK BODY at thermal equilibrium will emit radiation with INFINITE POWER. Max Planck resolved this issue by postulating that electromagnetic energy did not follow the classical description, but could only oscillate or be emitted in DISCRETE PACKETS OF ENERGY proportional to the frequency. He called these packets ‘QUANTA’. Note:

The Photoelectric Effect Einstein The emission of electrons from a surface (usually metallic) upon exposure to, and absorption of, electromagnetic radiation. The photoelectric effect was explained mathematically by Einstein who extended the work on QUANTA as developed by Planck.

Homework Complete Past Paper Question – may need to look up answer to part (b)! Complete worksheet but not questions that are crossed out – don’t need to know that bit! I will post a link to some useful online notes over the weekend on Unit 1 page. I will collect and mark next Thursday.

Definitions (From Past Papers) The Work Function:- minimum energy to remove an electron from the surface of a metal The Threshold Frequency:- minimum frequency of electromagnetic radiation required to eject photoelectrons from a metal surface

Photon Energy Recall from Particle Physics – Lesson 3 – Photons:- The energy of an incoming photon is given by The energy of an incoming photon is given by Where E is the Energy of Photon in Joules (J) Where E is the Energy of Photon in Joules (J) f is the Frequency of the radiation in Hertz (Hz) f is the Frequency of the radiation in Hertz (Hz) λ is the wavelength of the radiation in metres (m) λ is the wavelength of the radiation in metres (m) h is Planck’s constant = 6.63 × Js h is Planck’s constant = 6.63 × Js

More Equations The process of tearing an electron loose takes up an amount of energy called the work function,Φ, and the rest is converted into kinetic energy, E K(max) So when emission occurs we use Einstein’s equation:- So when emission occurs we use Einstein’s equation:- Or in Symbols:-

Analogies If you’re stuck down a well you can’t get out unless you have enough energy to jump out in one go – same for an electron. If you’re stuck down a well you can’t get out unless you have enough energy to jump out in one go – same for an electron. Coconut Shy – can fire 1,000 ping pong balls at a coconut – but they’re just ping pong balls, not going to knock the coconut off! Coconut Shy – can fire 1,000 ping pong balls at a coconut – but they’re just ping pong balls, not going to knock the coconut off! It only takes one bullet though...that does have enough energy and momentum It only takes one bullet though...that does have enough energy and momentum

What’s going on?

More Equations When the light incident on the metal is at exactly the threshold frequency the photons have just enough energy to free the electrons (i.e. the work function) When the light incident on the metal is at exactly the threshold frequency the photons have just enough energy to free the electrons (i.e. the work function) In Symbols:- where f 0 is the threshold frequency.

A further note... Photoelectrons are emitted with a range of KE from 0 up to a maximum which increases as the frequency increases. Nothing to do with intensity. Photoelectrons are emitted with a range of KE from 0 up to a maximum which increases as the frequency increases. Nothing to do with intensity. Why? Why?

Range of KE of Released Electrons

Conduction Electrons Conduction electrons move around randomly with energies ~6 × J  Conduction electrons move around randomly with energies ~6 × J  Work functions of metals are about J so conductions electrons do not have enough kinetic energy (KE) to escape. Work functions of metals are about J so conductions electrons do not have enough kinetic energy (KE) to escape. If an electron absorbs a photon with energy less than the work function it collides repeatedly with other electrons and positive ions and loses its extra KE. If an electron absorbs a photon with energy less than the work function it collides repeatedly with other electrons and positive ions and loses its extra KE.

Millikan’s Experiment Light enters through the filter. Light enters through the filter. Electrons go from cathode  anode. Electrons go from cathode  anode. Causes current measured by ammeter. Causes current measured by ammeter. You don’t need to know the details of the experiment for the exam, just the outcomes.

Determination of h Millikan’s experiment can be used to determine the maximum kinetic energy of the electrons. Millikan’s experiment can be used to determine the maximum kinetic energy of the electrons. A potential difference is applied across the phototube until zero current is measured. A potential difference is applied across the phototube until zero current is measured. This repeated for different frequencies of light, f and E K, max is measured for each value of f. This repeated for different frequencies of light, f and E K, max is measured for each value of f.

Graph of E max against freq.

Equation of a Straight Line The graph plotted is a straight line in the form of: Where m is the gradient and c is the y-intercept. Comparison with the straight line equation:- We can see that a graph of E K,max vs f, will result in a straight line with gradient = h and intercept = -φ