If the maximum speed of the emitted photoelectrons is 3.87 × 10° m/s, what wavelength of electromagnetic radiation s surface and caused the ejection of the photoelectrons?

Question

wavelength = m

Answer 1

If the maximum speed of the emitted photoelectrons is 3.87 × 10° m/s, what wavelength of electromagnetic radiation s surface and caused the ejection of the photoelectrons?

Bryan, I think you have left out a key piece of info about the metal (?) surface, i.e. the work function of the surface. Also, do you really intend for the photoelectron "speeding" at 3.87 m/s ?

In any case, here is the necessary set-up for the problem:

Let W = work function of the surface in Joules

E_ph = energy of the EM radiation

KE = kinetic energy of ejected photoelectrons

Then KE = E_ph - W (1)

Note that KE = 0.5 * m * V² , where V = the electron speed = 3.87 m/s

m = the mass of an electron = 9.11E-31 kg

Also note that E_ph = h * c / λ , where h = Planck's const. = 6.626E-34 Joule-sec

c = speed of light = 2.99E+8 m/s

λ = photon wavelength in meters

Now we have all we need to calculate the wavelength λ (except for the unknown work function of the surface!). Just plug in numbers and solve for the wavelength,

The flip side of this problem is how work functions are measured, by dialing up photon energies (shorter wavelengths using a type of spectrophotometer) until the threshold for photoelectrons is reached.