Certainly! To find the kinetic energy of the electron in a silicon atom when it absorbs a photon of a given energy, we can use the photoelectric equation derived from the conservation of energy.
The photoelectric equation is given by:
[tex]\[ K_{\text{max}} = E_{\text{photon}} - \phi \][/tex]
Where:
- [tex]\( K_{\text{max}} \)[/tex] is the maximum kinetic energy of the emitted electron.
- [tex]\( E_{\text{photon}} \)[/tex] is the energy of the incoming photon.
- [tex]\( \phi \)[/tex] is the work function of the material (the minimum energy needed to remove an electron from the material).
For the silicon atom:
- The work function ([tex]\( \phi \)[/tex]) is given as 1.1 eV.
- The photon energy ([tex]\( E_{\text{photon}} \)[/tex]) is given as 4.2 eV.
Now, let's calculate the kinetic energy step-by-step:
1. Write the photoelectric equation:
[tex]\[ K_{\text{max}} = E_{\text{photon}} - \phi \][/tex]
2. Substitute the given values into the equation:
[tex]\[ K_{\text{max}} = 4.2 \, \text{eV} - 1.1 \, \text{eV} \][/tex]
3. Perform the subtraction to find the kinetic energy:
[tex]\[ K_{\text{max}} = 4.2 \, \text{eV} - 1.1 \, \text{eV} = 3.1 \, \text{eV} \][/tex]
So, the kinetic energy of the electron is:
[tex]\[ K_{\text{max}} = 3.1 \, \text{eV} \][/tex]
Therefore, when a silicon atom absorbs a photon with an energy of 4.2 eV, the kinetic energy of the emitted electron will be 3.1 eV.
