22.2 The Photoelectric Effect

Why Emission of Photoelectrons is Dependent on Frequency and not Intensity

• Electron needs a minimum energy to escape.
• Instead of accumulating energy continuously, an electron absorbs a single whole packet.
• A packet’s energy is directly proportional to frequency and independent of intensity.
• Intensity relates to the number of packets per unit time.

How Photon Model of EM Radiation explains Threshold Frequency

• Electron needs a minimum energy to escape.
• Under the photon mode, electromagnetic radiation consists of discrete packets.
• The energy of a packet is directly proportional to frequency of electromagnetic radiation.
• An electron absorbs a single whole packet.
• Therefore, the absorbed packet must have the minimum energy, hence why a minimum frequency is needed.

Why $E_{k_{max}}$ is independent of the intensity of incident radiation

• Maximum kinetic energy of a photoelectron depends on the energy of the absorbed photon.
• The energy of an individual photon is directly proportional to frequency of EM radiation but independent of Intensity.
• Intensity relates to the number of photons incident per unit time.

Why do most electrons have kinetic energy less than $E_{k_{max}}$?

• Some energy is required to bring electrons to the surface.

S25 42 9

$V_s$ is the voltmeter reading at which the current just falls to zero. Explain with reference to photons, why $V_s$ depends on the frequency of the incident electromagnetic radiation.

• The current falls to zero when the potential difference $V_s$ equals the maximum kinetic energy per unit charge of the emitted electrons. ($E_{k_{max}}=e{V}_s$)
• The maximum kinetic energy of an emitted electron depends on the energy of the absorbed photon.
• The energy of an incident photon is directly proportional to frequency of the radiation ($E=hf$).

Explanation:

• In order for the current to be zero, no photoelectrons must be able to cross the gap between plate Y and plate X to complete the circuit.
• In order to ensure that no electrons reach plate X, all of them must be stopped, including the ones with maximum kinetic energy ($E_{k_{max}}$).
• The electric field between the two plates does work against the motion of the electrons to stop them.
• To just stop all the electrons, the electric field must do work that is equal to $E_{k_{max}}$.
• Since $V=\frac{W}{Q}$, $V_s=\frac{E_{k_{max}}}{e}$, $E_{k_{max}}=e{V}_s$.
• Therefore, the stopping potential $V_s$ must be equal to the maximum kinetic energy per unit charge of the electron.
• Maximum kinetic energy depends on energy of absorbed photon.
• Energy of an absorbed photon is directly proportional to frequency of electromagnetic radiation.
• Therefore, $V_s$ depends on the frequency of incident electromagnetic radiation.