The kinetic energy (KE) of the emitted electron can be calculated using the photoelectric effect formula, which is given by:
\[ KE = E_{photon} - \phi \]
where:
- \(KE\) is the kinetic energy of the electron,
- \(E_{photon}\) is the energy of the incoming photon, and
- \(\phi\) is the work function of the material.
In this case:
- \(E_{photon} = 4.2 , eV\)
- \(\phi = 1.1 , eV\)
Now, substituting in the values:
\[ KE = 4.2 , eV - 1.1 , eV \]
Calculating:
\[ KE = 3.1 , eV \]
Thus, the kinetic energy of the electron is \(3.1 , eV\).