What is the maximum kinetic energy of an ejected electron if silver metal is irradiated with 228-nm light? The threshold wavelength for a silver metal surface is 267 nm.
figure the energy in a photon of 228nm light, then subtract the work function energy equivalent to 267nm light.
To calculate the maximum kinetic energy of an ejected electron, we need to use the equation for the energy of a photon:
E = hc/λ
where:
E is the energy of the photon,
h is Planck's constant (6.626 x 10^-34 J·s),
c is the speed of light (3.00 x 10^8 m/s), and
λ is the wavelength of the light.
From the given information, the wavelength of the incident light is 228 nm (or 228 x 10^-9 m), and the threshold wavelength for silver metal is 267 nm (or 267 x 10^-9 m).
First, let's calculate the energy of the incident light:
E_incident = (6.626 x 10^-34 J·s) * (3.00 x 10^8 m/s) / (228 x 10^-9 m)
E_incident ≈ 8.71 x 10^-19 J
Now, let's calculate the energy corresponding to the threshold wavelength:
E_threshold = (6.626 x 10^-34 J·s) * (3.00 x 10^8 m/s) / (267 x 10^-9 m)
E_threshold ≈ 7.86 x 10^-19 J
Finally, we can calculate the maximum kinetic energy of the ejected electron using the equation:
K.E. = E_incident - E_threshold
K.E. ≈ (8.71 x 10^-19 J) - (7.86 x 10^-19 J)
K.E. ≈ 0.85 x 10^-19 J
Therefore, the maximum kinetic energy of the ejected electron is approximately 0.85 x 10^-19 J.
To find the maximum kinetic energy of an ejected electron, we can use the equation:
Kinetic Energy = Photon Energy - Work Function
1. Find the energy of a photon using the formula:
Energy of photon = (Planck's constant * Speed of Light) / Wavelength
Given that the wavelength of the light is 228 nm and Planck's constant (h) is approximately 6.626 × 10^-34 J·s, and the speed of light (c) is approximately 3.0 × 10^8 m/s, we can calculate the energy of the photon in Joules.
Energy of photon = (6.626 × 10^-34 J·s * 3.0 × 10^8 m/s) / (228 × 10^(-9) m)
2. Calculate the work function using the threshold wavelength:
Energy of threshold wavelength = (Planck's constant * Speed of Light) / Threshold Wavelength
Given that the threshold wavelength is 267 nm, we can calculate the energy of the threshold wavelength in Joules.
Energy of threshold wavelength = (6.626 × 10^-34 J·s * 3.0 × 10^8 m/s) / (267 × 10^(-9) m)
3. Calculate the maximum kinetic energy of the ejected electron:
Maximum Kinetic Energy = Energy of photon - Energy of threshold wavelength
Substitute the values obtained in the previous steps into the equation to find the maximum kinetic energy in Joules.
Finally, convert the Joules to electron volts (eV) by dividing by the elementary charge, which is approximately 1.6 × 10^-19 C.
Remember to always perform the necessary unit conversions to ensure consistency among the quantities used in the calculation.
Keep in mind that these calculations are theoretical and consider ideal conditions. In practice, other factors such as experimental setup and uncertainties might affect the results.