De Broglie and other Quantum Questions

[DizzyDoo]

Hi, just some quantum physics questions. I've given them all a good go, the first two just require checking, but the rest I'm rather stuck on. They're the last questions in about 20 other ones, and my head now hurts. :(

Any hints are very much appreciated!

Homework Statement

17. Metal X has a work function of 5.0 eV and is used in a demonstration of the photoelectric effect.
a) What is the min. frequency needed to remove electrons from X?

I firstly got converted the 5eV to joules which gave m 8 x 10^-19. I then divided that by the Planck's constant to get my final answer of 1.21 x 10¹⁵Hz

b) What is the wavelength of these waves?

I got the wavelength of 2.49 x 10^-7, by dividing the speed of an EM wave by the answer to A.

c) If metal X was irradiated with EM waves of frequency 2.0 x 1015 Hz, what will be the maximum kinetic energy of the photoelectrons released?

I'm afraid this is where I get stuck. The possible equations that I know are KE = 0.5mv² and hf = φ + ½ mv²_max but here I am unsure of the theory. :(

18. In the following two situations, calculate the de Broglie wavelength and, hence, state whether the particle or the wave model should be used.
a) Neutrons (m=1.8x10^-28kg) moving at 107ms^-1 passing a gap of 8x10^-10m

Pretty sure this is the particle model. Unsure of how to calculate the wavelength though, any ideas?

b) Electrons with a momentum of 4x10^-19kgms-1 passing nuclei diameter 10^-15m

I'm pretty sure this is the wave model. Same as the previous question.

Thanks for reading!

 

[dx]

17 c: If you supply energy hf to the electron, and W of this energy is used up to remove it from the metal, how much of the energy is left as kinetic energy?

18 a: The de Broglie wavelength is given by p = h/λ.