Calculating Maximum Resolution of Electron Microscope

In summary, the maximum possible resolution in an electron microscope is determined by the electron's momentum, which can be found using the equation p=mv. The voltage used to accelerate the electrons, in this case 2450 V, can be converted to joules using the equation 1 V = 1 J/C. The electron's momentum can then be used to calculate its wavelength using the de Broglie equation λ=h/p. The units for the maximum resolution will depend on the units used in the calculations, but it is typically measured in meters.
  • #1
Airplane7
15
0

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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  • #2
Hint #1: deBroglie
Hint #2: Rayleigh
 
  • #3
rude man said:
Hint #1: deBroglie
Hint #2: Rayleigh

Thanks, Can you help me with the problem though? I'm confused..
 
  • #4
So by using deBroglie equation lambda=h/p.. i'd have to do
6.63x10^-34Js / ((9.11x10^-31)(1.60x10^-19)) ??
 
  • #5
when i find the solution, do i multiply the answer by 2450? to get the maximum resolution?
 
  • #6
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.
 
  • #7
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.
 
  • #8
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?
 
  • #9
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!
 

1. How is the maximum resolution of an electron microscope calculated?

The maximum resolution of an electron microscope is calculated using the formula: R = 0.61λ/(NA), where R is the resolution, λ is the wavelength of the electrons, and NA is the numerical aperture of the objective lens. The higher the numerical aperture, the better the resolution.

2. What is the wavelength of electrons used in electron microscopes?

Electron microscopes use electrons with a wavelength of around 0.005 nanometers (nm). This is much smaller than the wavelength of visible light, which is around 400-700 nm, allowing for a much higher resolution.

3. How does the maximum resolution of an electron microscope compare to that of a light microscope?

The maximum resolution of an electron microscope is much higher than that of a light microscope. Light microscopes have a maximum resolution of around 200 nm, while electron microscopes can reach resolutions of less than 0.1 nm.

4. Can the maximum resolution of an electron microscope be improved?

Yes, the maximum resolution of an electron microscope can be improved by using a higher voltage, a smaller beam diameter, or a better objective lens with a higher numerical aperture. However, there is a limit to how much the resolution can be improved due to physical limitations.

5. What factors can affect the maximum resolution of an electron microscope?

The maximum resolution of an electron microscope can be affected by several factors, including the voltage and current of the electron beam, the quality and alignment of the lenses, the stability of the instrument, and the sample preparation techniques. Additionally, factors such as contamination or damage to the sample can also impact the resolution.

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