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Question

An electron is accelerated through a potential difference of 10,000 V. Its de Broglie wavelength is, (nearly) :
$$(m_e = 9 \times 10^{-31} kg)$$

A
$$12.2 \times 10^{-14} m$$
B
$$12.2 \times 10^{-12} m$$
C
$$12.2 \times 10^{-13} m$$
D
$$12.2 nm$$
Solution
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Correct option is B. $$12.2 \times 10^{-12} m$$
For an electron accelerated through a potential V,

$$\lambda = \dfrac{12.27}{\sqrt{V}} \mathring { A } $$

$$= \dfrac{12.27 \times 10^{-10}}{\sqrt{10000}}$$

$$ = 12.27 \times 10^{-12} m$$

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