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’

1900 - RayleighThis 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’.

hfE Note: sJxh .10626.6 34

hfKE

The Photoelectric Effect1905 - 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 EnergyPhoton Energy Recall from Particle Physics – Lesson 3 –

Photons:- The energy of an incoming photon is given byThe 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 f is the Frequency of the radiation in Hertz

(Hz)(Hz) λλ is the wavelength of the radiation in metres is the wavelength of the radiation in metres

(m)(m) h is Planck’s constant = 6.63 h is Planck’s constant = 6.63 ×× 10 10-34-34 Js Js

hc

hfE

More EquationsMore 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, EK(max)

So when emission occurs we use So when emission occurs we use Einstein’s equation:-Einstein’s equation:-

Or in Symbols:-(max)KEhf

Energy(J)KineticMaximum(J)FunctionWork(J)EnergyPhoton

AnalogiesAnalogies

If you’re stuck down a well you can’t get If you’re stuck down a well you can’t get out unless you have enough energy to jump out unless you have enough energy to jump out in one go – same for an electron.out in one go – same for an electron.

Coconut Shy – can fire 1,000 ping pong Coconut Shy – can fire 1,000 ping pong balls at a coconut – but they’re just ping balls at a coconut – but they’re just ping pong balls, not going to knock the coconut pong balls, not going to knock the coconut off!off!

It only takes one bullet though...that does It only takes one bullet though...that does have enough energy and momentumhave enough energy and momentum

What’s going on?What’s going on?

More EquationsMore Equations When the light incident on the metal is at When the light incident on the metal is at

exactly the threshold frequency the exactly the threshold frequency the photons have just enough energy to free photons have just enough energy to free the electrons (i.e. the work function)the electrons (i.e. the work function)

In Symbols:-

where f0 is the threshold frequency.

0hf

(J)EnergyPhoton)(JFunctionWork

A further note...A further note...

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

Why?Why?

Range of KE of Released Electrons

Conduction ElectronsConduction Electrons

Conduction electrons move around Conduction electrons move around randomly with energies ~6 × 10randomly with energies ~6 × 10-21 -21 J J

Work functions of metals are about 10Work functions of metals are about 10-19 -19 J J so conductions electrons do not have so conductions electrons do not have enough kinetic energy (KE) to escape.enough kinetic energy (KE) to escape.

If an electron absorbs a photon with energy If an electron absorbs a photon with energy less than the work function it collides less than the work function it collides repeatedly with other electrons and repeatedly with other electrons and positive ions and loses its extra KE.positive ions and loses its extra KE.

Millikan’s ExperimentMillikan’s Experiment

Light enters Light enters through the filter.through the filter.

Electrons go from Electrons go from cathode cathode anode. anode.

Causes current Causes current measured by measured by ammeter.ammeter.

You don’t need to know the details of the experiment for the exam, just the outcomes.

Determination of hDetermination of h

Millikan’s experiment can be used to Millikan’s experiment can be used to determine the maximum kinetic energy of determine the maximum kinetic energy of the electrons.the electrons.

A potential difference is applied across the A potential difference is applied across the phototube until zero current is measured.phototube until zero current is measured.

This repeated for different frequencies of This repeated for different frequencies of light, f and Elight, f and EK,K, max max is measured for each is measured for each value of f.value of f.

Graph of Emax 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 EK,max vs f, will result in a straight line with gradient = h and intercept = -φ

hfEK max,

cmxy