Photoelectric Effect

Instructor: Kazumi Tolich Lecture 21

¨ 28.2 The photoelectric effect ¤ Characteristics of the photoelectric effect ¤ Understanding the photoelectric effect ¤ Einstein’s explanation ¤ Einstein’s postulates and the photoelectric effect

¨ 28.3 Photons ¤ Detecting photons Quiz: 28.2-1

¨ In a photoelectric experiment, a current is detected when ultraviolet light shines on the metal cathode. What is the source or cause of the current?

A. The battery B. The light C. The cathode Quiz: 28.2-1 answer

¨ The light is the source or cause of the current.

¨ The emission of electrons from a substance due to light striking its surface is called the photoelectric effect.

¨ Electrons are emitted only if the light frequency � exceeds a threshold frequency �. The value of the threshold frequency depends on the type of metal from which the cathode is made. Quiz: 28.2-2

¨ In a photoelectric experiment, a current is detected when ultraviolet light shines on the metal cathode. What happens to the current if the battery voltage is reduced to zero?

A. The current is unchanged. B. The current decreases slightly. C. The current becomes zero. D. The current goes the other direction. Quiz: 28.2-2 answer

¨ What happens to the current if the � battery voltage is reduced to zero?

¨ The current decreases slightly.

¨ If the potential difference ∆� is more than about +1 V, the current ∆� changes very little as ∆� is −� 0 increased.

¨ If ∆� is negative, the current decreases to zero at stopping potential �. Quiz: 28.2-3

� ¨ The figure shows the photoelectric current vs. the applied potential difference in a photoelectric effect � apparatus. If the intensity of the light is reduced by 50%, how does the current vs. applied potential difference graph look? ∆� 0 � � �

� � �

∆� ∆� ∆�

0 0 0 A. B. C. Quiz: 28.2-3 answer

¨ The current is directly proportional to the light intensity.

¨ The value of stopping potential is independent of the intensity of light.

� �

∆� ∆�

0 0 A. 28.2 Understanding the photoelectric effect

¨ The work function of a metal is the minimum energy � needed to free an electron.

¨ The maximum possible kinetic energy of an ejected electron with energy � inside a metal is

� = � − �

¨ Measuring the stopping potential tells us the maximum kinetic energy of the electrons.

� � = � Quiz: 28.2-4

� ¨ The figure shows the photoelectric current vs. the applied potential difference in a photoelectric effect � apparatus. What happens to this graph if the cathode’s work function is slightly increased? ∆�

0 � � �

� � �

∆� ∆� ∆�

0 0 0 A. B. C. Quiz: 28.2-4 answer

¨ What happens to this graph if the cathode’s work function is slightly increased?

¨ The number of photoelectrons is unchanged as the intensity of light is unchanged.

¨ Electrons emerge slower, so stopping potential is reduced.

¨ � = =

� �

∆� ∆� −� −� 0 0 C. 28.2 Einstein’s postulates and the photoelectric effect

¨ Einstein framed three postulates about light quanta , photon, and their interaction with matter: 1. The energy of a photon is given by

� = ℎ�

where ℎ = 6.63×10 J s = 4.14×10 eV s is the Planck’s constant, and � is the frequency of the light. Each photon travels at the speed of light �. 2. Light quanta are emitted or absorbed on an all-or-nothing basis. 3. A light quantum, when absorbed by a metal, delivers its entire energy to one electron. Quiz: 28.2-5

¨ Monochromatic light shines on the cathode in a photoelectric effect experiment, causing the emission of electrons. If the number of photons per unit time hitting the cathode surface stays the same but the frequency of the light shining on the cathode is increased, what will happen? Choose all that apply. A. There will be more electrons emitted. B. There will be less electrons emitted. C. The emitted electrons will be moving at a higher speed. D. The emitted electrons will be moving at a slower speed. E. None of the above will happen. Quiz: 28.2-5 answer

¨ If the number of photons per unit time hitting the cathode surface stays the same but the frequency of the light shining on the cathode is increased, the emitted electrons will be moving at a higher speed.

¨ Each photon transfers its entire energy to just one electron.

¨ � = � − � = ℎ� − � ¨ If the frequency of the light stays the same but the intensity of the light shining on the cathode is increased instead, there will be more electrons emitted. Quiz: 28.2-6

� ¨ The figure shows the photoelectric current vs. the applied potential difference in a photoelectric effect � apparatus. What happens to this graph of the photoelectric current if the cathode’s work function is larger than the photon energy? ∆� 0 � � �

� � �

∆� ∆� ∆�

0 0 0 A. B. C. Quiz: 28.2-6 answer

¨ What happens to this graph of the photoelectric current if the cathode’s work function is larger than the photon energy?

¨ An electron can escape from the metal only if its energy exceeds the work function �, or if � = ℎ� ≥ �. ¨ There is a threshold frequency for the ejection of electrons: � = . � �

� = ℎ� − � � �

The slope is ℎ.

∆� ∆�

0 0 � A. 28.3 Photons

¨ If we conducted a double-slit experiment with a very dim light such that one photon passes through the double slit at a time, we see dots forming interference fringes.

¨ Each photon goes through both slits and interferes with itself.

¨ Sometimes light exhibits particle-like behavior and sometimes it exhibits wave-like behavior. Quiz: 28.3-1

¨ Points 1 and 2 are 5 µm apart. Light with a wavelength of 1 µm travels from point 1 to point 2. Which is the trajectory followed by the photons? A.

C. Quiz: 28.3-1 answer

¨ Points 1 and 2 are 5 µm apart. Light with a wavelength of 1 µm travels from point 1 to point 2. Which is the trajectory followed by the photons?

¨ Photons travel in straight lines. A.

C. 28.3 Detecting photons

¨ Examples of photon detectors are everywhere. ¤ Solar cell ¤ Charge-coupled device (CCD) or complementary metal oxide semiconductor (CMOS) detector in a digital camera n Press a button on your remote control and take a picture of it. The picture will show the infrared emitted by the remote, though this signal is invisible to your eye. ¤ Photo-multiply tubes (PMTs) can detect single photons and are widely used in experimental nuclear and particle physics.

SuperKamiokande detector Quiz: 28.3-2

¨ Port-wine birthmarks can be removed by exposure to 585 nm laser light. Pulses are strongly absorbed by oxyhemoglobin in the capillaries in the birthmark, destroying them. A typical laser pulse lasts for 1.5 ms, and contains an energy of 7.0 J. How many photons are in each pulse? Quiz: 28.3-2 answer

¨ The energy of a single 585 nm photon is .× ⁄ � = ℎ� = ℎ = 6.63×10 J s = 3.4×10 J × ¨ To get 7 J with this photon energy, = 2.1×10 photons are .× needed.