the work function for metallic Caesium is 2.14 eV. Calculate the kinetic energy and the speed of the electrons ejected by light of wavelength 700 nm
The photon energy is h*c/(wavelength) = 2.84*10^-19 J = 1.77 eV
Unless I made an error somewhere, there is not enough energy in a photon of that wavelength to eject a photoelectron.
2.8397j
To calculate the kinetic energy of the electrons ejected, we can use the equation:
Kinetic energy (K.E.) = Energy of light (E) - Work Function (W.F.)
First, let's convert the wavelength of light from nm to meters:
Wavelength (λ) = 700 nm = 700 x 10^(-9) m
Next, we can determine the energy of light using the equation:
Energy of light (E) = Planck's constant (h) x Speed of light (c) / Wavelength (λ)
Planck's constant (h) = 6.626 x 10^(-34) J·s
Speed of light (c) = 3 x 10^8 m/s
Plugging in the values:
E = (6.626 x 10^(-34) J·s) x (3 x 10^8 m/s) / (700 x 10^(-9) m)
Now, let's calculate the kinetic energy:
K.E. = (E) - (2.14 eV)
To convert electron volts (eV) to joules (J), we can use the conversion factor of 1 eV = 1.6 x 10^(-19) J.
Finally, we can calculate the speed of the ejected electrons using the equation for kinetic energy:
K.E. = (1/2)mv^2
where m is the mass of an electron and v is its velocity.
Let's solve for v:
v = sqrt((2K.E.) / m)
The mass of an electron (m) is approximately 9.11 x 10^(-31) kg.
Now, let's calculate the values step-by-step:
1. Convert wavelength to meters:
λ = 700 x 10^(-9) m
2. Calculate the energy of light (E):
E = (6.626 x 10^(-34) J·s) x (3 x 10^8 m/s) / (700 x 10^(-9) m)
3. Convert work function (W.F.) to joules:
W.F. = 2.14 eV x (1.6 x 10^(-19) J/eV)
4. Calculate the kinetic energy (K.E.):
K.E. = E - W.F.
5. Calculate the speed of the ejected electrons (v):
v = sqrt((2K.E.) / m)
Let's calculate the values:
To calculate the kinetic energy of the ejected electrons, we can use the equation:
Kinetic energy = Photon energy - Work function
We first need to find the energy of the photon using the equation:
Photon energy = (Planck's constant * Speed of light) / Wavelength
Let's calculate step by step:
Step 1: Convert the wavelength from nanometers (nm) to meters (m).
700 nm = 700 * 10^(-9) m
Step 2: Calculate the energy of the photon.
Photon energy = (6.626 x 10^(-34) J·s * 3 x 10^8 m/s) / (700 x 10^(-9) m)
Now we have the energy of the photon. Let's calculate it:
Photon energy = 2.839 x 10^(-19) J
Step 3: Calculate the kinetic energy of the ejected electrons.
Kinetic energy = Photon energy - Work function
To convert the work function from eV to Joules, we use the conversion factor:
1 eV = 1.6 x 10^(-19) J
Now let's calculate the kinetic energy:
Kinetic energy = 2.839 x 10^(-19) J - (2.14 eV * 1.6 x 10^(-19) J/eV)
Finally, we can calculate the speed of the ejected electrons using the equation:
Kinetic energy = (1/2) * (Mass of electron) * (Speed)^2
Let's continue with the calculations assuming the mass of the electron is 9.11 x 10^(-31) kg.
Step 4: Rearrange the equation to solve for Speed:
Speed = sqrt((2 * Kinetic energy) / Mass of electron)
Plug in the values:
Speed = sqrt((2 * Kinetic energy) / (9.11 x 10^(-31) kg))
Now you can calculate the kinetic energy and the speed of the ejected electrons by substituting these values into the equations.