Final answer:
In this case, the work function of the metal is approximately 1.87 eV. The work function of a metal can be calculated using the difference between the energy of the incident photon and the maximum kinetic energy of the photoelectron.
Step-by-step explanation:
The maximum kinetic energy of a photoelectron at the metal surface is the difference between the energy of the incident photon and the work function of the metal.
The work function is the binding energy of electrons to the metal surface.
First, we need to find the energy of the incident photon.
The energy of a photon is given by the equation E = hf, where E is the energy, h is Planck's constant (6.63 x 10-34 J s), and f is the frequency of the radiation.
We can find the frequency using the formula c = λf, where c is the speed of light (3 x 108 m/s) and λ is the wavelength of the radiation.
Given that the wavelength of the radiation is 6561 Å (1 Å = 10-10 m), we can calculate the frequency. f = c / λ. Substituting the values, we get
f = (3 x 108 m/s) / (6561 x 10-10 m)
= 4.57 x 1016 Hz.
Now we can find the energy of the photon.
E = hf
= (6.63 x 10-34 J s)(4.57 x 1016 Hz)
= 3.03 x 10-17 J
= 1.89 eV.
The maximum kinetic energy of the photoelectron is then given by Kmax = E - φ, where φ is the work function of the metal.
Rearranging the equation, we can solve for the work function.
φ = E - Kmax
= 1.89 eV - 10-19 J
= 1.89 eV - (1.6 x 10-19 J/eV)(1.89 eV).
Evaluating the expression, we find that the work function of the metal is approximately 1.87 eV.