a) If the work function for a certain metal is 1.8 eV, What is the stopping potential for electrons ejected from the metal when light of wavelength 400 nm shines on the metal?
b) What is the maximum speed of the ejected electrons?
The energy of the photoemission electrons is
E = [ h*c/(wavelength)] - 1.8 V* e
(a) Divide that by electron charge (e) for the stopping potential.
(b) Use E = (1/2)m V^2 to solve for V
a) To find the stopping potential for electrons, we can use the equation:
Stopping Potential = Photon Energy - Work Function
First, we need to calculate the photon energy using the formula:
Photon Energy = (Planck's Constant * Speed of Light) / Wavelength
Given:
Work Function (ϕ) = 1.8 eV
Wavelength (λ) = 400 nm
Plugging these values into the equation, we have:
Photon Energy = (6.626 x 10^(-34) Js * 3 x 10^8 m/s) / (400 x 10^(-9) m)
Calculating the photon energy gives us:
Photon Energy = 4.95 x 10^(-19) J
Now, we can calculate the stopping potential:
Stopping Potential = Photon Energy - Work Function
Stopping Potential = (4.95 x 10^(-19) J) - (1.8 eV * 1.602 x 10^(-19) J/eV)
Converting the work function to joules and performing the calculation:
Stopping Potential = (4.95 x 10^(-19) J) - (2.8836 x 10^(-19) J)
Stopping Potential = 2.0664 x 10^(-19) J
So, the stopping potential for electrons ejected from the metal is 2.0664 x 10^(-19) J.
b) To find the maximum speed of the ejected electrons, we can use the equation for the kinetic energy of an electron:
Kinetic Energy (KE) = Stopping Potential = 1/2 mv^2
We can rearrange the equation to solve for the velocity (v):
v = sqrt((2 * Stopping Potential) / m)
Given:
Stopping Potential = 2.0664 x 10^(-19) J
Mass of an Electron (m) = 9.10938356 x 10^(-31) kg
Plugging in the values, we have:
v = sqrt((2 * 2.0664 x 10^(-19) J) / (9.10938356 x 10^(-31) kg))
Calculating the maximum speed of the ejected electrons gives us:
v ≈ 1.34 x 10^6 m/s
So, the maximum speed of the ejected electrons is approximately 1.34 x 10^6 m/s.
To answer these questions, we need to use the concept of the photoelectric effect and the equations related to it. The photoelectric effect refers to the emission of electrons from a material surface when electromagnetic radiation, such as light, is incident upon it.
a) To calculate the stopping potential, we need to find the minimum potential difference required to stop the ejected electrons. This can be calculated using the relationship:
Stopping Potential (V) = Energy of Incident Photon (E) - Work Function (W)
First, let's determine the energy of an incident photon using the equation:
Energy of a photon (E) = Planck's constant (h) * Frequency (f)
The frequency can be calculated using the speed of light equation:
Speed of light (c) = Wavelength (λ) * Frequency (f)
Therefore, the frequency is:
Frequency (f) = Speed of light (c) / Wavelength (λ)
Substituting the value of the speed of light (c = 3 * 10^8 m/s) and the given wavelength (400 nm = 400 * 10^(-9) m), we can calculate the frequency.
Now that we have the frequency, we can calculate the energy of the incident photon using Planck's constant (h = 4.136 * 10^(-15) eV s).
Finally, we can calculate the stopping potential by subtracting the work function from the energy of the incident photon.
b) To find the maximum speed of the ejected electrons, we can use the equation for kinetic energy:
Kinetic Energy (K.E.) = Energy of incident photon - Work Function
The kinetic energy can be related to the maximum speed (v) of the electrons using the equation:
Kinetic Energy (K.E.) = (1/2) * mass of electron (m) * (maximum speed)^2
Solving for the maximum speed (v), we can calculate its value.
Let's go through the calculations step-by-step to find the answers to both questions.