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What is the de Broglie wavelength of an electron accelerated from rest through a potential difference of 50.0 V?
(a) 0.100 nm
(b) 0.139 nm
(c) 0.174 nm
(d) 0.834 nm
(e) none of those answers

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Answer:

(c) 0.174 nm

Explanation:

According to de Broglie hypothesis, the wavelength of the wave associated with electron is given by:

[tex] \boxed{ \bf{\lambda = \sqrt{\dfrac{150}{V \ (in \ Volt)}} \: \text{\AA}}}[/tex]

V → Potential Difference (50.0 V)

By substituting value of potential difference in the equation, we get:

[tex] \rm \longrightarrow \lambda = \sqrt{\dfrac{150}{50}} \: \text{\AA} \\ \\ \rm \longrightarrow \lambda = \sqrt{3} \: \text{\AA} \\ \\ \rm \longrightarrow \lambda = 1.74 \: \text{\AA} \\ \\ \rm \longrightarrow \lambda = 0.174 \: nm[/tex]

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