The resolution limit of a microscope is roughly equal to the wavelength of light

Question

The resolution limit of a microscope is roughly equal to the wavelength of light used in producing the image. Electron microscopes use an electron beam (in place of photons) to produce much higher resolution images, about 0.23nm in modern instruments. Part A Assuming that the resolution of an electron microscope is equal to the de Broglie wavelength of the electrons used, to what speed must the electrons be accelerated to obtain a resolution of 0.23nm ? Express your answer to two significant figures and include the appropriate units. ve = Item 18 An electron in the n=7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 93.1 nm. Part B What is the value of n for the level to which the electron relaxed? Express your answer as an integer. n = Part C What is the de Broglie wavelength of an electron traveling at 1.08 The resolution limit of a microscope is roughly equal to the wavelength of light used in producing the image. Electron microscopes use an electron beam (in place of photons) to produce much higher resolution images, about 0.23nm in modern instruments. Part A Assuming that the resolution of an electron microscope is equal to the de Broglie wavelength of the electrons used, to what speed must the electrons be accelerated to obtain a resolution of 0.23nm ? Express your answer to two significant figures and include the appropriate units. ve = Assuming that the resolution of an electron microscope is equal to the de Broglie wavelength of the electrons used, to what speed must the electrons be accelerated to obtain a resolution of 0.23nm ? Express your answer to two significant figures and include the appropriate units. ve = ve = ve = Item 18 An electron in the n=7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 93.1 nm. Item 18 An electron in the n=7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 93.1 nm. An electron in the n=7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 93.1 nm. An electron in the n=7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 93.1 nm. Part B What is the value of n for the level to which the electron relaxed? Express your answer as an integer. n = Part B What is the value of n for the level to which the electron relaxed? Express your answer as an integer. n = n = n = Part C What is the de Broglie wavelength of an electron traveling at 1.08 ve =

Explanation / Answer

? = h/mv
Rearrange and solve for v, the velocity:
v = h/m?
For this problem we have
? = 0.23 nm = 2.3 x 10^-10 m
h= Planck's constant = 6.626

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