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 calculate the maximum kinetic energy of an ejected electron, we can use the equation:
E = h * c / 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),
and λ is the wavelength of the light.
Given:
Wavelength of light (λ) = 228 nm = 228 x 10^-9 m
First, let's determine the energy of the incoming photon using the equation:
E = h * c / λ
E = (6.626 x 10^-34 J s) * (3.0 x 10^8 m/s) / (228 x 10^-9 m)
Calculating this, we find:
E ≈ 2.76 x 10^-19 J
Next, we need to find the threshold energy for silver which corresponds to a wavelength of 267 nm:
Threshold wavelength (λ_threshold) = 267 nm = 267 x 10^-9 m
Now, let's determine the energy of the photon at the threshold wavelength:
E_threshold = h * c / λ_threshold
E_threshold = (6.626 x 10^-34 J s) * (3.0 x 10^8 m/s) / (267 x 10^-9 m)
Calculating this, we find:
E_threshold ≈ 2.34 x 10^-19 J
The maximum kinetic energy of an ejected electron can be calculated as the difference between the energy of the incoming photon and the threshold energy:
Kinetic energy (K.E.) = E - E_threshold
K.E. = (2.76 x 10^-19 J) - (2.34 x 10^-19 J)
Calculating this, we find:
K.E. ≈ 4.2 x 10^-20 J
Therefore, the maximum kinetic energy of the ejected electron is approximately 4.2 x 10^-20 J.
To find the maximum kinetic energy of an ejected electron when silver metal is irradiated with 228-nm light, we need to use the concept of the photoelectric effect and the equation for the energy of a photon.
The photoelectric effect states that when light of a certain frequency or wavelength is incident on a metal surface, electrons can be ejected from the metal if the energy of the photons is sufficient to overcome the binding energy of the electrons. The ejected electrons then acquire kinetic energy due to the absorption of the photon's energy.
First, we can find the energy of a photon using the equation:
E = hc/λ
Where:
E is the energy of the photon
h is Planck's constant (6.62607015 × 10^-34 J·s)
c is the speed of light (2.998 × 10^8 m/s)
λ is the wavelength of light in meters
Using the given wavelength, we can calculate the energy of the photons:
E = (6.62607015 × 10^-34 J·s * 2.998 × 10^8 m/s) / (228 × 10^-9 m)
E ≈ 8.70 × 10^-19 J
Next, we need to find the threshold energy. The threshold wavelength for silver metal is given as 267 nm. We can convert this to meters and calculate the corresponding threshold energy using the same equation:
E_threshold = (6.62607015 × 10^-34 J·s * 2.998 × 10^8 m/s) / (267 × 10^-9 m)
E_threshold ≈ 7.45 × 10^-19 J
Finally, to find the maximum kinetic energy of the ejected electron, we subtract the threshold energy from the energy of the photon:
K_max = E - E_threshold
K_max ≈ (8.70 × 10^-19 J) - (7.45 × 10^-19 J)
K_max ≈ 1.25 × 10^-19 J
Therefore, the maximum kinetic energy of an ejected electron when silver metal is irradiated with 228-nm light is approximately 1.25 × 10^-19 J.