In a photoelectric effect experiment red light with a wavelength of 7.01 x 10^-7 m is able to emit an electron with a maximum kinetic energy of 1.02 x 10^-19. What is the binding energy of the electron?
KE = hc/lambda - BE.
You are given KE of 1.02E-19 J
You are given lambda of 7.01E-7 m. You know the constants h and c. Solve for the BE (I call that this the work function). Post your work if you get stuck. The solution appears to be straight forward to me.
To determine the binding energy of the electron, we need to use the photoelectric effect equation:
E = hc/λ - Φ
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 (3.00 x 10^8 m/s)
λ is the wavelength of the light
Φ is the work function or binding energy of the electron
Given:
λ = 7.01 x 10^-7 m
E = 1.02 x 10^-19 J
First, we need to calculate the energy of the photon using the equation E = hc/λ:
E = (6.626 x 10^-34 J·s)(3.00 x 10^8 m/s)/ (7.01 x 10^-7 m)
E ≈ 2.833 x 10^-19 J
Next, rearrange the photoelectric effect equation to solve for the binding energy:
Φ = hc/λ - E
Φ = (6.626 x 10^-34 J·s)(3.00 x 10^8 m/s)/ (7.01 x 10^-7 m) - 1.02 x 10^-19 J
Φ ≈ 2.833 x 10^-19 J - 1.02 x 10^-19 J
Φ ≈ 1.813 x 10^-19 J
Therefore, the binding energy of the electron is approximately 1.813 x 10^-19 J.
To find the binding energy of the electron in the photoelectric effect experiment, we can use the equation:
Kinetic energy of the electron = Binding energy - Work function
In this equation, the kinetic energy of the electron is given as 1.02 x 10^-19 J.
The work function represents the amount of energy required to remove an electron from the surface of a material in the experiment. In this case, it is assumed that the work function is zero since the wavelength of the red light is lower than the threshold wavelength needed to eject electrons.
Therefore, the equation becomes:
1.02 x 10^-19 J = Binding energy - 0
Simplifying the equation further, we find that the binding energy is equal to the kinetic energy of the electron:
Binding energy = 1.02 x 10^-19 J
Hence, the binding energy of the electron is 1.02 x 10^-19 J.