Calculating Maximum Resolution of Electron Microscope

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Homework Help Overview

The problem involves calculating the maximum possible resolution of an electron microscope, given that electrons are accelerated by 2450 V. The discussion centers around the application of de Broglie's wavelength equation and the relationship between momentum and energy in the context of electron microscopy.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of the de Broglie equation to find the wavelength of electrons and question how to relate voltage to momentum. There are attempts to clarify the distinction between voltage and velocity, and confusion arises regarding the calculations involved in determining momentum and resolution.

Discussion Status

The discussion is active, with participants sharing their attempts at calculations and seeking clarification on concepts. Some guidance has been provided regarding the relationship between energy, momentum, and the equations needed to approach the problem, though confusion remains about specific steps and interpretations.

Contextual Notes

Participants express uncertainty about the definitions and relationships between voltage, energy, and momentum, indicating a need for further exploration of these concepts. The original poster is new to the forum and is navigating the expectations of the homework context.

Airplane7
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Homework Statement


Electrons are accelerated by 2450 V in an electron microscope. What is the maximum possible resolution?
Me=9.11 x 10^-31kg and e= 1.60 x 10^-19 C


Homework Equations


I'm not so sure which equations to use for this question.. maybe the Planck's formula?
λ=h/p

The Attempt at a Solution

 
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Hint #1: deBroglie
Hint #2: Rayleigh
 
rude man said:
Hint #1: deBroglie
Hint #2: Rayleigh

Thanks, Can you help me with the problem though? I'm confused..
 
So by using deBroglie equation lambda=h/p.. i'd have to do
6.63x10^-34Js / ((9.11x10^-31)(1.60x10^-19)) ??
 
when i find the solution, do i multiply the answer by 2450? to get the maximum resolution?
 
Airplane7 said:
So by using deBroglie equation lambda=h/p.. i'd have to do
6.63x10^-34Js / ((9.11x10^-31)(1.60x10^-19)) ??
No. Why would you multiply m and e? It doesn't make any sense.
 
Moderator's note: I have moved this thread to Introductory Physics. In the future, please post questions of this level in Introductory Physics.

The information given for V can be used to find p.
 
vela said:
No. Why would you multiply m and e? It doesn't make any sense.

Lol, I'm not sure.. I'm confused on solving the question..

So, to find p, it's p=mv right? so (9.11 x 10^-31kg)(2450 v) ?

When i find the solution of p, plug it into lambda=h/p, so (6.63x10^-34 Js) / p , will give me the maximum resolution?
 
Redbelly98 said:
Moderator's note: I have moved this thread to Introductory Physics. In the future, please post questions of this level in Introductory Physics.

The information given for V can be used to find p.

Thank you. Sorry, I'm new to the forum
 
  • #10
Airplane7 said:
Lol, I'm not sure.. I'm confused on solving the question..

So, to find p, it's p=mv right? so (9.11 x 10^-31kg)(2450 v) ?
No. The v in p=mv represents the velocity of the particle. The V in 2450 V stands for volt; it's a unit of electric potential. They're not the same thing at all.

Read about electric potential in your textbook so you understand what the problem means when it says "Electrons are accelerated by 2450 V."

When i find the solution of p, plug it into lambda=h/p, so (6.63x10^-34 Js) / p , will give me the maximum resolution?
That's the basic idea, but you need to find the electron's momentum first.
 
  • #11
Okay. I read up on it, but it didn't say much on "electrons accelerating"
I did see that 1 Volt = 1 J/C
So 2450 V = 2450 J/C
(1.60x10^-19 C)(2450 J/C) = ??

Man.. i am so confused
 
  • #12
Okay. This is what I got, tell me if i did it correctly.

E= (1.60x10^19C)(2450J/C) = 3.92x10-16 J
V= Squareroot of √(2x3.92x10^-16) / (9.11x10^-31) = 2.93x10^7

So using de Broglie equation

lambda= (6.63x10^-34Js)/(9.11x10^-31)(2.93x10^7) = 2.48x10^-11 ?
 
  • #13
10^11? That's way off!

(Right method, though.)
 
  • #14
Lol, aw man.. I thought I had it in the bag. What did I do wrong?
 
  • #15
Wait.. I wrote, 10^-11, not 10^11. Am I still wrong?
 
Last edited:
  • #16
I see you edited your original answer so it says 10^-11 now instead of 10^11. That would be the right answer if you included the units.
 
  • #17
Thank you for all your help!

Would the units be in meters?
 
  • #18
You tell me. :)
 
  • #19
I guess so! :) Thanks for your help!
 

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