Question

Considering only the effect of diffraction, and assuming that the resolution is equal to the deBroglie wavelength, what is the smallest structure resolvable using a 12 keV electron microscope?

1.15 × 10^-11 m

1.23 × 10^-11 m

1.12 × 10^-11 m

1.14 × 10^-11 m

Answer 1

Solution:

In general, the resolving power of any microscope depends on the wavelength (of light or matter waves). The smallest structure has the dimension equal to or greater than the wavelength used.

In our case, if we find the de-Borglie wavelength of 12 keV electrons, we can find the dimensions of the smallest structure that can be resolved by the electron microscope.

The electron has the kinetic energy of 12 keV and it is very less as compared to its rest energy (0.511Mev). So we can ignore relativistic effects and use classical equations for momentum and kinetic energy.

Since we are given kinetic energy of electron, we can find its momentum and later use it to find the deBorglie wavelength.

We note that mass of electron is m = 9.11*10^-31kg and

electron-volt to joules conversion is,

12 keV = 12000 eV = 12000 eV*(1.60*10^-19 J/eV)

Hence the third choice 1.12*10^-11 m is correct.

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It is evident that other choices are not correct.