First slide

Matter waves (DC Broglie waves)

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 eV is so directed that it passes through the holes. When it comes out its de-Broglie wavelength is

Moderate

A

1.22 $\overset{o}{A}$
B

1.75 $\overset{o}{A}$
C

2 $\overset{o}{A}$
D

None of these

Solution

Energy of the electron, when it comes out from the second plate = 200 V- 100 V = 100 V
Hence accelerating potential difference = 100 V
$λ_{electron} = \frac{12 .27}{\sqrt{V}} = \frac{12 .27}{\sqrt{100}} = 1 .23 \overset{o}{A}$

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