The threshold wavelength of zinc is 390 nm.
1) Find the frequency of zinc
2) What is the work function in eVerything of zinc?
3) Zinc in a photocell is irradiated u ultraviolet light of 260 nm wavelength. What is the kinetic energy of the photoelectrons in eV?
1. f=c/wavelength
3. Workfunction=plancksconst*freq
3. figure the energy of 250 nm light, subtracat the work function, then the remainder energy is KE
1) To find the frequency of zinc, we can use the equation:
frequency (ν) = speed of light (c) / wavelength (λ)
Given that the threshold wavelength of zinc is 390 nm, we can convert it to meters:
wavelength (λ) = 390 nm = 390 x 10^-9 meters
The speed of light (c) is approximately 3 x 10^8 meters per second.
Substituting these values into the equation, we get:
frequency (ν) = (3 x 10^8 m/s) / (390 x 10^-9 m)
= 7.7 x 10^14 Hz
Therefore, the frequency of zinc is 7.7 x 10^14 Hz.
2) The work function (Φ) represents the minimum amount of energy required to remove an electron from the surface of a material.
The energy (E) of a photon is given by the equation:
energy (E) = Planck's constant (h) x frequency (ν)
Given that we know the frequency of zinc is 7.7 x 10^14 Hz, we can find the energy of the photon. Planck's constant (h) is approximately 6.626 x 10^-34 J s.
Substituting these values into the equation, we get:
energy (E) = (6.626 x 10^-34 J s) x (7.7 x 10^14 Hz)
= 5.1 x 10^-19 J
To convert the energy from joules to electron volts (eV), we use the conversion factor:
1 eV = 1.602 x 10^-19 J
Therefore, the work function of zinc is approximately 3.2 eV (5.1 x 10^-19 J / 1.602 x 10^-19 J).
3) The kinetic energy of the photoelectrons can be calculated using the equation:
kinetic energy (K.E.) = energy of incident photon - work function
We can find the energy of the incident photon using the equation mentioned in the previous step:
energy (E) = (6.626 x 10^-34 J s) x (speed of light (c) / wavelength (λ))
Given that the wavelength of the ultraviolet light is 260 nm, we can convert it to meters:
wavelength (λ) = 260 nm = 260 x 10^-9 meters
Substituting these values into the equation, we get:
energy (E) = (6.626 x 10^-34 J s) x (3 x 10^8 m/s) / (260 x 10^-9 m)
= 7.6 x 10^-19 J
Now we can calculate the kinetic energy:
kinetic energy (K.E.) = energy of incident photon - work function
= (7.6 x 10^-19 J) - (5.1 x 10^-19 J)
≈ 2.5 x 10^-19 J
To convert the kinetic energy from joules to electron volts (eV), we use the conversion factor:
1 eV = 1.602 x 10^-19 J
Therefore, the kinetic energy of the photoelectrons is approximately 1.56 eV (2.5 x 10^-19 J / 1.602 x 10^-19 J).