Evans SPH 4U1

Unit 9: Quantum Theory

Note 3: The Photoelectric Effect - Continued

Reference: Chapter 12.1

Refer to the seven observation points on The Photoelectric Effect from Note 2.

Only part of the first point could be explained on the basis of classical wave theory (i.e. above the threshold frequency, the more intense the light, the greater the photoelectron current). None of the other observations could be explained. For example,

• It didn't make sense that a high intense beam of low frequency light couldn't produce a photoelectric current.

• It also didn't make sense that a the intensity of the light did not affect the maximum Ek of the ejected photoelectrons.

Boat Analogy:

In classical wave theory, a wave of small amplitude (low intensity) could never toss a boat onto the shore regardless of the frequency of the waves.

However, point 2 says that even a small amplitude (low intensity) wave could toss a boat onto the shore (i.e. eject a photoelectron) if the frequency is high enough. This is against classical wave theory.

Photons:

Einstein therefore proposed that the energy of electromagnetic radiation, is not a continuous wave, but is concentrated in bundles called photons.

When a photon hits a photoelectric surface, a surface electron absorbs its energy.  Some of the energy is needed to release the electron and the remaining energy becomes the Ek of the ejected photoelectron.

1. He was able to explain threshold frequency..... The energy of the photons must exceed the energy needed to escape the attractive forces holding it to the metal.  When the frequency of the light is too low, the photon does not provide the absorbing electron with enough energy and it remains bound to the surface.

2. Einstein's model said that more intense light only means more photons. The energy of each photon is not affected (it depends only on the frequency).

where Ephoton is the energy of the incident photon

W is the energy with which the electron is bound to the surface( also called Work function)

Ek is the kinetic energy of the ejected photoelectron

Rearranging to get Einstein's Photoelectric Equation::

Note: In the threshold case Ek = 0.

where fo is the threshold frequency

Refer back to your 12.1.1 lab of kinetic energy versus frequency. The y intercept was the work function and the x intercept was the threshold frequency.

In 1921 Einstein received the Nobel Prize in Physics for his explanation of the photoelectric effect.

Problem 1:

EM radiation of frequency 7.0 X 1014 Hz falls on a metal with work function of 0.5eV.

a) Calculate the maximum kinetic energy of the emitted photoelectrons and the maximum speed of the emitted photoelectrons.

(Answer: 3.8 x 10 –19 J)

NOTE: Remind students if questions ask for speed make sure you convert everything into Joules.

b) What would be the case if the kinetic energy was less than 0.5 eV. (Answer: no emission)

Problem 2:

Calculate the Threshold (minimum) frequency for a metal with a work function or binding energy of 1.5 eV. (Answer: 3.6 x 1014 Hz)

Problem 3:

A photoelectric surface has a work function of 1.50 eV.  A red light of wavelength 650 nm is directed the the surface. Calculate:

a) The maximum Ek of the emitted photoelectrons in joules (Answer: 6.60 x 10 -20 J)

b) The photoelectrons' maximum speed (Answer:  3.81 x 10 5 m/s)

c) The cutoff potential needed to stop the photoelectrons (Answer: 0.412 V)

Suggested Textbook Questions:

Page 604 #'s 10-15

Applications:

• Burglar alarms and automatic door openers make use of a photocell circuit and a beam of light. When the beam of light is broken, the current suddenly drops to zero and this activates a switch such as a solenoid which controls the alarm or door.

• Calculators equipped with photocells do not require a battery. They can function if enough light falls on the photoelectric surface.