You are working as a demonstration assistant for a physics professor. She wants to demonstrate to her students the buildup of the interference pattern for single electrons passing through a double slit. Her source of electrons will be a certain vacuum tube, in which electrons evaporate from a hot cathode at a slow, steady rate and accelerate from rest through a potential difference of 45.0 V. After being accelerated, they travel through a fieldfree and evacuated region before they pass through the double slits and fall on a screen to produce an interference pattern. To ensure that only one electron at a time is passing through the slits, she wants the electrons to be separated in space by d 5 1.00 cm (perpendicular to the barrier containing the slits) as they approach the slit. She asks you to determine the maximum value for the beam current that will assure that only one electron at a time passes through the slits.

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Asked Nov 14, 2019
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You are working as a demonstration assistant for a physics professor. She wants to demonstrate to her students the buildup of the interference pattern for single electrons passing through a double slit. Her source of electrons will be a certain vacuum tube, in which electrons evaporate from a hot cathode at a slow, steady rate and accelerate from rest through a potential difference of 45.0 V. After being accelerated, they travel through a fieldfree and evacuated region before they pass through the double slits and fall on a screen to produce an interference pattern. To ensure that only one electron at a time is passing through the slits, she wants the electrons to be separated in space by d 5 1.00 cm (perpendicular to the barrier containing the slits) as they approach the slit. She asks you to determine the maximum value for the beam current that will assure that only one electron at a time passes through the slits.

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Expert Answer

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Step 1

Given information

V=45V

d=1cm

Step 2

The Potential difference provides the velocity to the electron. So, apply conservation of energy and plug the required values to find the velocity (v) of the electron (mass (m) of the electron is 9.11x10-31 kg and electronic charge (e) is 1.6x10-19 C).

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= eV 2eV V т (1.6x10 19C (451) 9.11x10-31kg v 3.98x106m/s

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Step 3

Write the formula for linear current density (λ) and plug the required values to find the li...

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1.6x1019C 1m 1cm 100cm 2 =1.6X107C/m

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