Question

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

Answer 1

(c) 0.174 nm

Step-by-step explanation:

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

`\boxed{ \bf{\lambda = \sqrt{(150)/(V \ (in \ Volt))} \: \text{\AA}}}`

V → Potential Difference (50.0 V)

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

`\rm \longrightarrow \lambda = \sqrt{(150)/(50)} \: \text{\AA} \\ \\ \rm \longrightarrow \lambda = √(3) \: \text{\AA} \\ \\ \rm \longrightarrow \lambda = 1.74 \: \text{\AA} \\ \\ \rm \longrightarrow \lambda = 0.174 \: nm`