To tackle this question, we need to delve into the photoelectric effect and the concept of stopping potential in a photoelectric cell. The photoelectric effect describes how photons can eject electrons from a material, and the energy of the emitted electrons depends on the energy of the incident photons and the work function of the material. Let's break this down step by step.
Understanding the Photoelectric Effect
When photons strike a cathode, they can transfer their energy to electrons. If the energy of the photon exceeds the work function (the minimum energy required to remove an electron from the material), electrons are emitted. The energy of the emitted electrons can be calculated using the formula:
E_k = E_photon - φ
Where:
- E_k = kinetic energy of the emitted electron
- E_photon = energy of the incident photon
- φ = work function of the material
Analyzing the Given Data
In your scenario, we have two different photon energies: 5 eV and 6 eV. Let's analyze each case:
Case 1: 5 eV Photons
When photons with an energy of 5 eV hit the cathode, the maximum kinetic energy of the emitted photoelectrons is given as 2 eV. Using the formula above, we can find the work function:
2 eV = 5 eV - φ
Rearranging gives us:
φ = 5 eV - 2 eV = 3 eV
Case 2: 6 eV Photons
Now, when 6 eV photons are incident on the cathode, you mentioned that no photoelectrons reach the anode. This implies that the energy of the emitted electrons is insufficient to overcome the stopping potential created by the anode. The stopping potential is the potential difference that needs to be applied to prevent the emitted electrons from reaching the anode.
Using the same work function we calculated earlier (3 eV), we can find the kinetic energy of the emitted electrons when 6 eV photons are used:
E_k = 6 eV - 3 eV = 3 eV
Determining the Stopping Potential
Since the emitted electrons have a maximum kinetic energy of 3 eV, the stopping potential (V_s) needed to prevent these electrons from reaching the anode can be calculated using the relationship:
eV_s = E_k
Where e is the charge of the electron (which we can consider as 1 for simplicity in this context). Thus, we have:
V_s = 3 V
Final Thoughts
In summary, the stopping potential of the anode relative to the cathode is 3 volts. This means that a potential difference of 3 volts must be applied to prevent the emitted electrons from reaching the anode when 6 eV photons are incident on the cathode. Understanding these principles helps clarify how energy transfer works in photoelectric cells and the role of stopping potential in controlling electron flow.
