Textbook Q 1B.15 part c

[Vance Liu]

Question:

The velocity of an electron that is emitted from a metallic surface by a photon is 3.6x10^3 km/s. (a) What is the wavelength of the ejected electron? (b) No electrons are emitted from the surface of the metal until the frequency of the radiation reaches 2.5x10^16 Hz. How much energy is required to remove the electron from the metal surface? (c) What is the wavelength of the radiation that caused photoejection of the electron? (d) What kind of electromagnetic radiation was used?

Answer: 8.8 nm

I just assumed that if the frequency of the incident radiation is 2.5x10^16 Hz, then it is a relatively simple calculation to get the wavelength (speed of light/frequency). However my answer (1.2*10^-8 m) is clearly not correct so am I missing something? I also tried the work function energy and it didn't work (Ephoton-Ework=Ekinetic energy of e-)

[Nancy Li 1C]

You should have been able to use the equation Ephoton - work function = Ek. Rearranging the equation, we get that Ephoton = work function + Ek. From the previous part b, we know that the work function is 1.66 x 10^-17 J so we have Ephoton = 1/2mv^2 + 1.66 x 10^-17 J. Plugging in the velocity that was given (converted to m/s) and the mass of an electron (9.11x10^-31 kg) to find the kinetic energy, we get the overall Ephoton to be 2.25 x 10^-17 J. Using hc/λ, we can solve for the wavelength, which should come out to the 8.8 nm.

[Vance Liu]

You should have been able to use the equation Ephoton - work function = Ek. Rearranging the equation, we get that Ephoton = work function + Ek. From the previous part b, we know that the work function is 1.66 x 10^-17 J so we have Ephoton = 1/2mv^2 + 1.66 x 10^-17 J. Plugging in the velocity that was given (converted to m/s) and the mass of an electron (9.11x10^-31 kg) to find the kinetic energy, we get the overall Ephoton to be 2.25 x 10^-17 J. Using hc/λ, we can solve for the wavelength, which should come out to the 8.8 nm.

Alright thanks, I probably just inputted it wrong or something.