Light with a wavelength of 405 nm fell on a strontium surface, and electrons were ejected. If the speed of an ejected electron is 3.39 105 m/s, what energy was expended in removing the electron from the metal?
(1/2*m*v^2)= hc/wavelength)-phi
Solve for phi, the work function.
m = mass electrons.
v = speed electron
h = Planck's constant'
c = speed of light in m/s
wavelength in meters.
phi will be energy in J/photon.
how do you know what the mass electrons is?
To determine the energy expended in removing an electron from a metal, we can use the equation:
E = hf - Φ
Where:
E is the energy expended in removing the electron,
h is the Planck's constant (6.626 x 10^-34 J s),
f is the frequency of the light,
Φ is the work function, which represents the minimum energy required to remove an electron from the metal.
First, we need to convert the wavelength of light (λ) to frequency (f) using the equation:
c = λf
Where:
c is the speed of light (3.00 x 10^8 m/s)
λ is the wavelength of light
f is the frequency of light
Plugging in the values, we get:
f = c/λ
f = (3.00 x 10^8 m/s)/(405 x 10^-9 m)
= 7.41 x 10^14 Hz
Next, we can calculate the energy using the equation:
E = hf - Φ
Given that the speed of the ejected electron is 3.39 x 10^5 m/s, we can use the kinetic energy formula:
KE = 1/2 mv^2
Rearranging to solve for m (mass):
m = 2KE/v^2
Plugging in the values, we get:
m = 2(1.6 x 10^-19 J)/(3.39 x 10^5 m/s)^2
≈ 3.92 x 10^-31 kg
Now, we can calculate the energy expended in removing the electron:
E = 1/2 mv^2 - Φ
Given that the speed of the ejected electron is 3.39 x 10^5 m/s and we know its mass,
E = 1/2 (3.92 x 10^-31 kg)(3.39 x 10^5 m/s)^2
- Φ
Substituting the calculated values, we can find the energy expended in removing the electron.