To understand the kinetic energy of photoelectrons emitted from a copper emitter when illuminated by monochromatic light, we need to consider several factors, including the work function of the material, the energy of the incoming photons, and the potential difference between the emitter and collector plates.
Understanding the Basics
The work function (Φ) of a material is the minimum energy required to remove an electron from the surface of that material. For copper, this value is given as 4.5 eV. When light shines on the emitter, photons can impart energy to electrons, potentially allowing them to escape if the energy exceeds the work function.
Calculating Photon Energy
The energy of a photon can be calculated using the formula:
E = \frac{hc}{\lambda}
Where:
- E = energy of the photon (in eV)
- h = Planck's constant (4.135667696 × 10^-15 eV·s)
- c = speed of light (approximately 3 × 10^8 m/s)
- λ = wavelength of the light (in meters)
For a wavelength of 200 nm (which is 200 × 10^-9 m), we can calculate the energy:
E = \frac{(4.135667696 × 10^{-15} eV·s)(3 × 10^8 m/s)}{200 × 10^{-9} m} ≈ 6.2 eV
Determining Kinetic Energy
The kinetic energy (KE) of the emitted photoelectron can be found using the equation:
KE = E - Φ + V
Where:
- E = energy of the incoming photon (6.2 eV)
- Φ = work function of copper (4.5 eV)
- V = potential difference between the emitter and collector (2 V)
Calculating Minimum Kinetic Energy
For the minimum kinetic energy, we can substitute the values:
KE_min = 6.2 eV - 4.5 eV - 2 V = 6.2 eV - 4.5 eV - 2 eV = -0.3 eV
Since kinetic energy cannot be negative, this indicates that no electrons would be emitted under these conditions, which means the minimum kinetic energy is effectively zero when considering the potential barrier.
Calculating Maximum Kinetic Energy
For the maximum kinetic energy, we consider the scenario where the electron has enough energy to escape the work function and is then accelerated by the potential difference:
KE_max = E - Φ + V = 6.2 eV - 4.5 eV + 2 eV = 3.7 eV
Summary of Energies
In summary, the minimum kinetic energy of the photoelectron is effectively zero, as the energy provided by the photon is not sufficient to overcome the work function and the potential barrier. The maximum kinetic energy, however, is calculated to be 3.7 eV, which accounts for the energy of the photon minus the work function, plus the energy gained from the potential difference between the plates.
This illustrates how both the properties of the material and the conditions of the experiment influence the behavior of photoelectrons in photoelectric experiments.
