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Electron Microscope

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Pupil
Karma Points: 60
Respect (83%):
Date Posted: 7/24/2008 4:33:24 AM  Status: Live
Electron Microscope
Course Textbook Chapter Problem
General Physics College Physics (8th) by Young N/A N/A
Question Details:
Intro:
An electron microscope is using a 1.00-keV electron beam. An atom has a diameter of about 10^{-10} meters.

Part A
What is the wavelength lambda of electrons in this microscope?
Express your answer in nanometers to three significant figures.
  lambda  =
  {\rm nm}

submithints

Part B
Can an individual atom theoretically be resolved using this electron microscope?
yes
no


submithints

Part C
Suppose we replace the electron beam with a proton beam. What proton energy is needed to achieve the same resolution as the electron beam in Part A?
Express your answer in electron volts to three significant digits.
  {\rm eV}

submithints



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Answers:

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Oracle
Karma Points: 8,304
Date Posted: 7/24/2008 11:46:22 AM  Status: Live
Asker's Rating: Somewhat Helpful   
Response:
λ = h/p ....... deBroglie
E = 0.5 mv^2 , p = momentum = mv
E = [m/2][p^2/m^2] = p^2/2m
p = [2mE]^1/2

Part A

λ = h/p = (h )/ (2mE)^1/2

E = (1*10^3) (1.6*10^-19 Joule) = 1.6*10^-16 J

λ = wavelength = (6.6*10^-34) / (2*9.1*10^-31)(1.6*10^-16)^1/2
λ= 3.868*10^-11 m = 0.0368 nm

Part B

Yes
Smaller the wavelength larger is the RP
0.38 *10^-10 < 1*10^-10

Part C

Mass pf proton mp = 1836 me
(0.0368*10^-9) = (h) / (2*1836)(9.1*10^-31)(E1)^1/2
Find E1
d0ve's Comment:
thank you
Hope this helps. Don't forget to rate the answer.



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