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Question

Two large parallel plates are connected with the terminal of $100 V$ power supply. These plates have a fine hole at the centre. An electron having energy $200 e V$ is so directed that it passes through the holes. When it comes out it's de-Broglie wavelength is

A

1.22 A^{\circ}

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B

1.75 A^{\circ}

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C

2 A^{\circ}

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D

none of these

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Solution

The correct option is A $1.22 A^{\circ}$
Energy of the electron, when it comes out from the second plate $= 200 e V - 100 e V = 100 e V$
Hence acceleration potential difference $= 100 V$
$λ_{E l e c t r o n} = \frac{12.27}{\sqrt{V}} = \frac{12.27}{\sqrt{100}} = 1.23 o A$

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