Find de Broglie Wavelength of 7.0 eV Electron

[Dart82]

Homework Statement

Find the de Broglie wavelength of a 7.0 eV electron.

Homework Equations

de Broglie wavelength = h/p = h/(mv)
Photoelectric effect equation (not 100% sure)

The Attempt at a Solution

i need to solve for v in de Broglie's equation so i can find the wavelength. i know the mass of the electron is 9.11x10^-31kg, i know that h is Plancks constant, and i know that the work function = 7.0 x (1.602x10^-19 J) BUT how can i find v?

I tried to find v by using the photoelectric effect equation but i didnt get a correct answer:
hf = KE + Work function...BUT how can i solve for v if i don't have the frequency!?

 

[Dick]

The energy of the electron is just given by E=(1/2)*m*v^2 (no need for relativity here). Does that help?

 

[Dart82]

Dick -
i wish i could tell you that it makes perfect sense now, but I'm still a bit confused here. When you say no relativity what exactly does that mean?

 

[Dick]

I mean the energy is low enough that the speed of the electron is much less than that of light. So I can use the nonrelativistic formula KE=(1/2)*m*v^2. Sorry to hear you are still confused, but why not just set 7eV equal to (1/2)*m*v^2 to find v?

 

[Dart82]

Sorry to hear you are still confused, but why not just set 7eV equal to (1/2)*m*v^2 to find v?

well...i guess because i don't understand how the work function can just be set to equal the kinetic energy. how is it that the hf can just be dropped from the photoelectric equation? I sure do wish my teacher would have spent some more time on this stuff - it seems like he just left out half the info we need to complete this assignment.

 

[Dart82]

Ok, i got the right answer but i only understand about 90% of what i did to get it. According the Photo. effect:
h*f - W = KE ...so then h*f - W = (1/2)mv^2
I guess my only question is where did the h and f disappear to?

 

[Dick]

Why do you think this is a photoelectric effect problem? There is no 'work function'. It's just a de Broglie wavelength problem.

 

[Dick]

Ok, i got the right answer but i only understand about 90% of what i did to get it. According the Photo. effect:
h*f - W = KE ...so then h*f - W = (1/2)mv^2
I guess my only question is where did the h and f disappear to?

There's no h*f in the problem either.

 

[Dart82]

ok i see what you are saying. i guess because the only other place i have seen the eV is in the photoelectric effect problems. i have read my notes and the section in my book concerning the de Broglie Wavelength (which there were no examples problems given). consequently, i am having a tough time figuring out how to work them. The way i understand it P=mv, where v is the speed. i know KE = (1/2)mv^2. So in this instance KE = 7eV?

 

[Dick]

Yes. In this case eV is just a unit of energy. I thought you were going to take a break.

 

[Dart82]

yes i am right now...

 

[Dick]

Me too...