# CIE A Level Physics复习笔记22.1.5 The Work Function

### Photoelectric Emission

• The work function Φ, or threshold energy, of a material is defined as:

The minimum energy required to release a photoelectron from the surface of a material

• Consider the electrons in a metal as trapped inside an ‘energy well’ where the energy between the surface and the top of the well is equal to the work function Φ
• A single electron absorbs one photon
• Therefore, an electron can only escape the surface of the metal if it absorbs a photon which has an energy equal to Φ or higher
• Different metals have different threshold frequencies, and hence different work functions
• Using the well analogy:
• A more tightly bound electron requires more energy to reach the top of the well
• A less tightly bound electron requires less energy to reach the top of the well In the photoelectric effect, a single photon may cause a surface electron to be released if it has sufficient energy

• Alkali metals, such as sodium and potassium, have threshold frequencies in the visible light region
• This is because the attractive forces between the surface electrons and positive metal ions are relatively weak
• Transition metals, such as manganese and iron, have threshold frequencies in the ultraviolet region
• This is because the attractive forces between the surface electrons and positive metal ions are much stronger

#### Laws of Photoelectric Emission

• Observation:
• Placing the UV light source closer to the metal plate causes the gold leaf to fall more quickly
• Explanation:
• Placing the UV source closer to the plate increases the intensity incident on the surface of the metal
• Increasing the intensity, or brightness, of the incident radiation increases the number of photoelectrons emitted per second
• Therefore, the gold leaf loses negative charge more rapidly
• Observation:
• Using a higher frequency light source does not change how quickly the gold leaf falls
• Explanation:
• The maximum kinetic energy of the emitted electrons increases with the frequency of the incident radiation
• In the case of the photoelectric effect, energy and frequency are independent of the intensity of the radiation
• So, the intensity of the incident radiation affects how quickly the gold leaf falls, not the frequency
• Observation:
• Using a filament light source causes no change in the gold leaf’s position
• Explanation:
• If the incident frequency is below a certain threshold frequency, no electrons are emitted, no matter the intensity of the radiation
• A filament light source has a frequency below the threshold frequency of the metal, so, no photoelectrons are released
• Observation:
• Using a positively charged plate causes no change in the gold leaf’s position
• Explanation:
• If the plate is positively charged, that means there is an excess of positive charge on the surface of the metal plate
• Electrons are negatively charged, so they will not be emitted unless they are on the surface of the metal
• Any electrons emitted will be attracted back by positive charges on the surface of the metal
• Observation:
• Emission of photoelectrons happens as soon as the radiation is incident on the surface of the metal
• Explanation:
• A single photon interacts with a single electron
• If the energy of the photon is equal to the work function of the metal, photoelectrons will be released instantaneously

### Intensity & Photoelectric Current

• The maximum kinetic energy of the photoelectrons is independent of the intensity of the incident radiation
• This is because each electron can only absorb one photon
• Kinetic energy is only dependent on the frequency of the incident radiation
• Intensity is a measure of the number of photons incident on the surface of the metal
• So, increasing the number of electrons striking the metal will not increase the kinetic energy of the electrons, it will increase the number of photoelectrons emitted

#### Photoelectric Current

• The photoelectric current is the number of photoelectrons emitted per second
• Photoelectric current is proportional to the intensity of the radiation incident on the surface of the metal
• This is because intensity is proportional to the number of photons striking the metal per second
• Since each photoelectron absorbs a single photon, the photoelectric current must be proportional to the intensity of the incident radiation Kinetic energy of photoelectrons is independent of intensity, whereas the photoelectric current is proportional to intensity and independent of frequency 