Textbook Problem 1B 15 [ENDORSED]

[Alison Le 2E]

Hi! Could someone help me solve part c and d? I already completed part a and b, but I'm stuck on how to do c. Thanks!

The velocity of an electron that is emitted from a metallic surface by a photon is 3.6*10^3 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 2.50 * 10^16 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?

[Shria G 2D]

Hi,

For part c, you would first need to find the total energy that was used to eject the electron and that can be found by adding the work function (which is the answer to part b) + kinetic energy of the electron. This is because the electron has velocity after it is ejected so that means more energy than just the minimum required to eject the electron was used.

To find the kinetic energy, I used the equation KE = 0.5mv^2 and I converted the given velocity from km to m before using it.
For the total energy, I ended up getting 2.25 x 10^-17 J.
I then converted it to wavelength using the equation E = h(c/lambda) and I got 8.8 x 10^-9 m which is 8.8 nm as the final answer.

For part d, I just found what region of the electromagnetic spectrum 8.8 nm corresponds to and it is the x-ray region.