Photoelectric effect example problem [ENDORSED]

[Stephanie tran 1J]

How do you solve a problem where the given information includes that an electron is ejected from a metal due to the photoelectric effect with a velocity in km per second and the work function is given, but you're supposed to calculate the wavelength of the photon absorbed.

[Brandon Fujii 1K]

Note the Photoelectric Effect equation: E_(Photon) - Work Function = E_(Kinetic).
E_(Kinetic) = 1/2 (m_e-v_e-²)

The equation for E_(Photon)= hv (Plank's Constant * Frequency)
We know that the equation for the speed of light is: C= Wavelength * Frequency.
Therefore, Frequency = C/Wavelength

If we substitute C/Wavelength for our Frequency we would get the following equation:

h(C/wavelength) - Work Function = 1/2 (m_e-v_e-²)

Thus: h(C/Wavelength) = [1/2 (m_e-v_e-²)]+Work Function

Wavelength= (hC)/[(1/2 (m_e-v_e-²)+Work Function]

*Make sure that your velocity of the electron is in meters/sec*

[jillian1k]

You would use the equation E(photon)-E(energy to remove e-)=E(excess), where E(photon)=hv, E(energy to remove e-) is also known as work function, and E(excess)=Ek=(1/2m)(v^2).
1.) Calculate Ek=(1/2m)(v^2) using the velocity(v) of e- given in the problem and the constant mass of an e- (9.109 383 × 10−31 kg), which will be given to you either in the problem or on the formula/constants sheet provided at every test.
2.) Now that you know the other two of the three variables in the equation for E(photon), calculate the E(photon).
3.) Using the number you got for E(photon), you can now calculate wavelength. This can be done in 2 ways. Either use the formula E=hv to get v and then plug that number into the equation for wavelength (λ=c/v). Or you can save a step and combine these two formulas into one (E=hc/λ) and solve for λ.
Note: c and h are constants and λ should be in m or nm.

Hope this helps!