The "work function", or the minimum energy needed to eject an electron from the metal, can be expressed in several different ways. As stated on the applet page, sodium has a work function of 2.75 eV. In class, we discussed how to determine what that work function was in terms of the wavelength of the light, and found that light of 450 nm was sufficient to eject an electron.
A.)What is the work function for cesium in nm?
b.)For a silver electrode (hint: click just below the word "cesium"), what is the maximum energy of an electron ejected by light of 250 nm? (answer in eV)
A) You are going to have to look up the work function in V before you can calculate the maximum allowed wavelength. It is about 1.9 V. Knowing the value for sodium won't help.
B) Calculate the energy associated with a 250 nm (ultraviolet) photon, using
E = hc/(wavelength)
Then subtract the work function energy of Cs, which is e*(work function in volts)
A.) To determine the work function for cesium in nm, we can use the equation:
Work Function (in eV) = Energy (in eV) / Charge (in e)
We know that the work function of sodium is 2.75 eV, and we can use this information to find the energy in eV associated with the wavelength of light that ejected an electron (450 nm).
Energy (in eV) = (Planck's constant * speed of light) / Wavelength (in nm)
Energy (in eV) = ((6.626 × 10^-34 J·s) * (3 × 10^8 m/s)) / (450 × 10^-9 m)
Converting the values, we get:
Energy (in eV) ≈ 2.769 eV
Now we can use this energy value and the charge of an electron (1.6 × 10^-19 C) in the equation to find the work function for cesium:
Work Function (in eV) = 2.769 eV / (1.6 × 10^-19 C)
Work Function (in eV) ≈ 1.731 × 10^20 eV
To convert this to nm, we can use:
Work Function (in nm) = (1240 eV * nm) / Work Function (in eV)
Plugging in the values, we find:
Work Function (in nm) ≈ (1240 eV * nm) / (1.731 × 10^20 eV)
Work Function (in nm) ≈ 7.16 × 10^-16 nm
Therefore, the work function for cesium in nm is approximately 7.16 × 10^-16 nm.
B.) To find the maximum energy of an electron ejected by light of 250 nm for a silver electrode, we can use the energy formula mentioned earlier:
Energy (in eV) = (Plank's constant * speed of light) / Wavelength (in nm)
Energy (in eV) ≈ ((6.626 × 10^-34 J·s) * (3 × 10^8 m/s)) / (250 × 10^-9 m)
Converting the values, we get:
Energy (in eV) ≈ 2.494 eV
Therefore, the maximum energy of an electron ejected by light of 250 nm for a silver electrode is approximately 2.494 eV.
To determine the work function for cesium in nm (question A), we need to use the relation between the work function and the wavelength of light. The equation we can use is:
Energy of a photon = h * c / λ
Here, h is Planck's constant (6.626 x 10^-34 J s), c is the speed of light (3.0 x 10^8 m/s), and λ is the wavelength of light in meters.
To convert the work function from eV to Joules, we can use the conversion factor: 1 eV = 1.602 x 10^-19 J.
Given that sodium has a work function of 2.75 eV, we can calculate the energy of a photon using the given wavelength of 450 nm (0.45 μm) as follows:
λ = 0.45 x 10^-6 m
Energy of a photon = (6.626 x 10^-34 J s * 3.0 x 10^8 m/s) / (0.45 x 10^-6 m)
Energy of a photon = 4.418 x 10^-19 J
Now we can equate the energy of a photon to the work function and solve for the work function of cesium (Φ):
Φ = Energy of a photon / (1.602 x 10^-19 J/eV)
Φ = 4.418 x 10^-19 J / (1.602 x 10^-19 J/eV)
Φ ≈ 2.76 eV
Therefore, the work function for cesium is approximately 2.76 eV.
Now let's move on to question B, which asks for the maximum energy of an electron ejected by light of 250 nm on a silver electrode.
Similar to the previous calculation, we can use the energy equation:
Energy of a photon = h * c / λ
Given that the wavelength of light is 250 nm (0.25 μm), we can calculate the energy of a photon using the same constants:
λ = 0.25 x 10^-6 m
Energy of a photon = (6.626 x 10^-34 J s * 3.0 x 10^8 m/s) / (0.25 x 10^-6 m)
Energy of a photon = 7.951 x 10^-19 J
To convert this energy to eV, we divide by the conversion factor:
Energy in eV = 7.951 x 10^-19 J / (1.602 x 10^-19 J/eV)
Energy in eV ≈ 4.96 eV
Therefore, the maximum energy of an electron ejected by light of 250 nm on a silver electrode is approximately 4.96 eV.