De Broglie Wavelength Calculation for an Electron with KE= 8.5 eV

AI Thread Summary
The discussion revolves around calculating the De Broglie wavelength of an electron with a kinetic energy of 8.5 eV. The user converted the energy to joules and calculated the velocity, momentum, and wavelength, arriving at a wavelength of approximately 4.209e-10 meters. Despite the calculations appearing correct, the user is unable to match the expected answer, which is in the order of picometers. There is a suggestion that the problem may involve a misunderstanding of energy units or a potential error in the homework system, as the kinetic energy is confirmed to be in eV, not keV. The conversation emphasizes the importance of maintaining precision in calculations to avoid errors in systems with strict rounding requirements.
starthorn
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Homework Statement


What is the De Broglie wavelength of an electron with KE= 8.5 eV?


Homework Equations


λ=h/p
KE=0.5mv2
p=mv


The Attempt at a Solution


I converted 8.5 eV into joules:
8/5 eV × 1.602e-19 J = 1.3617e-18

Then used it for KE to solve for v:
I got 1729006.11

Used v to get p:
9.11e-31 × 1729006.11 = 1.575e-24

Used p to get λ:
6.63e-34/1.575e-24

And received λ= 4.209e-10

The answer required is on the order of picometers, and when I convert it to pm the answer is wrong. Entering it as it is also comes up wrong.
Sorry I use excessive sigfigs, my homework is through the Connect system for my textbook and there is a VERY SMALL margin of error so you always have to keep a bunch of extra or the answer might come up as wrong if you round too early.
 
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You might need to use the relativistic momentum:
p=γm0v
(γ is the lorentz factor)
 
starthorn said:
What is the De Broglie wavelength of an electron with KE= 8.5 eV?

Are you sure it's not KE = 8.5 keV? Your calculations look OK.

The answer required is on the order of picometers

What is it?

Sorry I use excessive sigfigs,

Ideally you should not round at all until you reach the final answer, i.e. keep the intermediate numbers in your calculator as you go along. Or better yet, derive an equation that let's you plug in your given numbers and get the final answer immediately. But I don't think that's your problem.
 
Nessdude14 said:
You might need to use the relativistic momentum:
p=γm0v
(γ is the lorentz factor)
The hint portion of the problem states that it is not relativistic but I will check my calculations with it. Seeing as how the velocity I calculated is slightly under 0.006c though I am sure it is not.

jtbell said:
Are you sure it's not KE = 8.5 keV? Your calculations look OK.

Part a is in eV and part b is in keV, so yes I am sure


jtbell said:
What is it?
I can't see the answer without "giving up" on the problem, which means I will lose the credit for it. I know, it is an awful faulty system, but what can I do? It's the one my professor uses.
 
It's definitely not relativistic, as stated. 8.5 eV << 511 keV (the rest-energy of an electron).

Either you're missing something in the problem statement, or the answer in the "system" is simply wrong. Textbooks do sometimes have a wrong answer for a problem.

I tried using different units for the intermediate steps and I still get the same answer.
 

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