Through what potential difference must electrons be accelerated so that they will exhibit wave nature in passing through a pinhole 0.10 micrometers in diameter?

0.15 mV

Explanation:

In order to exhibit wave nature, the de Broglie wavelength of the electron must be of the same size of the diameter of the pinhole, therefore:

The de Broglie wavelength of an electron is

where

is the Planck constant

is the mass of the electron

v is the electron's speed

Therefore, the electron's speed must be

When accelerated through a potential difference , the kinetic energy gained by the electron is equal to the change in electric potential energy, therefore

where

is the magnitude of the charge of the electron

So, we can find the potential difference needed:

kepler used the data from tycho blahe (his mentor) to construct the laws of planetary motion.