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timama [110]
3 years ago
14

Through what potential difference must electrons be accelerated so that they will exhibit wave nature in passing through a pinho

le 0.10 micrometers in diameter?​
Physics
1 answer:
Mila [183]3 years ago
5 0

Answer:

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:

\lambda=0.10 \mu m = 1.0\cdot 10^{-7} m

The de Broglie wavelength of an electron is

\lambda = \frac{h}{mv}

where

h=6.63\cdot 10^{-34} Js is the Planck constant

m=9.11\cdot 10^{-31} kg is the mass of the electron

v is the electron's speed

Therefore, the electron's speed must be

v=\frac{h}{m\lambda}=\frac{6.63\cdot 10^{-34}}{(9.11\cdot 10^{-31})(1.0\cdot 10^{-7})}=7278 m/s

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

e\Delta V = \frac{1}{2}mv^2

where

e=1.6\cdot 10^{-19} is the magnitude of the charge of the electron

So, we can find the potential difference needed:

\Delta V=\frac{mv^2}{2e}=\frac{(9.11\cdot 10^{-31})(7278)^2}{2(1.6\cdot 10^{-19})}=1.5\cdot 10^{-4}V = 0.15 mV

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