To calculate the kinetic energy of the electron when a photon with energy is incident on the silicon atom, we can use the photoelectric effect equation:
\[ K.E. = E_{\text{photon}} - \phi \]
where:
- \( K.E. \) is the kinetic energy of the emitted electron,
- \( E_{\text{photon}} \) is the energy of the incoming photon,
- \( \phi \) is the work function of the material (energy needed to remove the electron from the atom).
In this case:
- \( E_{\text{photon}} = 4.2 , \text{eV} \)
- \( \phi = 1.1 , \text{eV} \)
Now, we can substitute these values into the equation:
\[ K.E. = 4.2 , \text{eV} - 1.1 , \text{eV} \]
Calculating this gives:
\[ K.E. = 3.1 , \text{eV} \]
Thus, the kinetic energy of the electron is \( 3.1 , \text{eV} \).