What is the deBroglie wove length of an electron traveling of 99.00% of the spee

Question

What is the deBroglie wove length of an electron traveling of 99.00% of the speed of light (mass of electron -9.1095 x 10^-31 kg? 1 0. The resolution limit of a microscope is roughly equal to the wavelength of light used in producing the image. Electron microscopes use on electron beam (in place of photons) to produce much higher resolution images. In modem electron microscopes, the resolution is about 0.20 nm. Assume that the resolution of an electron microscope is equal to the deBroglie wavelength of the electrons used. To what speed must the electrons be accelerated in order to obtain a resolution of 0.20 nm?

Explanation / Answer

ANSWER

09. de Brogle wavelength = h / mv

h = planks constant = 6.63 X 10-34Js

m = mass of the particle

v = velocity of the prticle = (2.99 X 108 ) X 99.0 / 100 = 2.96 X 108 m/s

= 6.62 X 10-34Js / 9.1095 X 10-31 X 2.96 X 108 m/s = 2.45 X 10-12m

1. As the resolution is equal to de Broglie wavelength we can use the aboveequation to find the required resolution

= h / mv

0.2 X 10-9 = 6.63 X 10-34Js  / 9.1095 X 10-31  X v

v = 6.62 X 10-34Js  / 9.1095 X 10-31 X 0.2 X 10-9 = 3.64 X 106 m/s

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