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.
To determine the maximum kinetic energy of an ejected electron when a metal is irradiated with light, we need to use the concept of the photoelectric effect. The photoelectric effect states that when light hits the surface of a metal, electrons can be emitted if the energy of the incident photons is greater than the work function (threshold energy) of the metal.
First, we need to calculate the energy of the incident photons with a wavelength of 228 nm. We can use the equation:
Energy = (Planck's constant * speed of light) / wavelength
The Planck's constant (h) is approximately 6.626 x 10^-34 J·s, and the speed of light (c) is approximately 3.0 x 10^8 m/s.
Energy = (6.626 x 10^-34 J·s * 3.0 x 10^8 m/s) / (228 x 10^-9 m)
= 2.755 x 10^-19 J
Next, we can compare this energy to the work function of silver metal, which has a threshold wavelength of 267 nm. We can calculate the threshold energy using the same formula:
Threshold Energy = (Planck's constant * speed of light) / threshold wavelength
Threshold Energy = (6.626 x 10^-34 J·s * 3.0 x 10^8 m/s) / (267 x 10^-9 m)
= 2.48 x 10^-19 J
Finally, we can calculate the maximum kinetic energy of the ejected electron by subtracting the threshold energy from the energy of the incident photons:
Maximum Kinetic Energy = Energy - Threshold Energy
= (2.755 x 10^-19 J) - (2.48 x 10^-19 J)
= 0.275 x 10^-19 J
= 2.75 x 10^-20 J
Therefore, the maximum kinetic energy of the ejected electron is approximately 2.75 x 10^-20 J.
To find the maximum kinetic energy of an ejected electron, we can use the equation for the energy of a photon and the relationship between energy and kinetic energy of an electron.
The energy of a photon can be calculated using the equation:
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 (3.0 x 10^8 m/s)
λ is the wavelength of light
For the maximum kinetic energy of an ejected electron, we can use the equation:
KE_max = E - E_threshold
Where:
KE_max is the maximum kinetic energy of the ejected electron
E is the energy of the incident photon
E_threshold is the threshold energy required to remove an electron from the metal surface
Given:
Wavelength of incident light (λ) = 228 nm = 228 x 10^-9 m
Threshold wavelength (λ_threshold) = 267 nm = 267 x 10^-9 m
First, let's calculate the energy of the incident photon:
E = hc/λ
E = (6.626 x 10^-34 J.s)(3.0 x 10^8 m/s)/(228 x 10^-9 m)
E ≈ 8.66 x 10^-19 J
Next, let's calculate the threshold energy:
E_threshold = hc/λ_threshold
E_threshold = (6.626 x 10^-34 J.s)(3.0 x 10^8 m/s)/(267 x 10^-9 m)
E_threshold ≈ 7.43 x 10^-19 J
Finally, we can find the maximum kinetic energy of the ejected electron:
KE_max = E - E_threshold
KE_max = (8.66 x 10^-19 J) - (7.43 x 10^-19 J)
KE_max ≈ 1.23 x 10^-19 J
Therefore, the maximum kinetic energy of the ejected electron is approximately 1.23 x 10^-19 Joules.