Light with a frequency of 4.32 × 1015 Hz strikes a metal surface and ejects electrons that have a maximum kinetic energy of 5.8 eV. What is the work function (in eV) of the metal?
figure the energy in each photon
energy=PlancksConstatn*(frequency.
work function=photonenergy-kemax
To find the work function of the metal in electron volts (eV), we can use the equation:
Energy of light photon = Work function + Maximum kinetic energy of ejected electrons
The energy of a photon can be calculated using the formula:
Energy of photon = Planck's constant × Frequency of light
Given that the frequency of the light is 4.32 × 10^15 Hz, and the maximum kinetic energy of ejected electrons is 5.8 eV, we can substitute the values into the equations to find the work function.
1. Planck's constant (h) is a physical constant: h = 4.135667696 × 10^-15 eV·s
2. Calculate the energy of the photon:
Energy of photon = Planck's constant × Frequency of light
Energy of photon = (4.135667696 × 10^-15 eV·s) × (4.32 × 10^15 Hz)
3. Substitute the value of the energy of the photon and the maximum kinetic energy of ejected electrons into the equation:
Energy of photon = Work function + Maximum kinetic energy of ejected electrons
(4.135667696 × 10^-15 eV·s) × (4.32 × 10^15 Hz) = Work function + 5.8 eV
4. Rearrange the equation to isolate the work function:
Work function = (4.135667696 × 10^-15 eV·s) × (4.32 × 10^15 Hz) - 5.8 eV
Now, we can calculate the work function:
Work function = (4.135667696 × 10^-15 eV·s) × (4.32 × 10^15 Hz) - 5.8 eV
Plug in the values and calculate the work function.