What is the speed of an electron whose de Broglie wavelength is $0.1 n m$ ? By what potential difference, must have such an electron accelerated from an initial speed zero?

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Solution

$λ = \frac{h}{m v}$ (Debroglie's equation)
$10^{- 10} = \frac{6.626 \times 10^{- 34}}{9.1 \times 10^{- 31} \times v} v = 7.28 \times 10^{6}$
Let potential difference be $Δ v$
$\frac{1}{2} {m v}^{2} = e Δ v$ (e=charge on $e^{-}$ )
$\frac{1}{2} \times \frac{9.1 \times 10^{- 31} \times 52.99 \times 10^{12}}{1.6 \times 10^{- 19}} = Δ v Δ v = 150 V o l t s$

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What is the speed of an electron whose de Broglie wavelength is 0.1nm? By what potential difference, must have such an electron accelerated from an initial speed zero?

λ=hmv(Debroglie's equation)10−10=6.626×10−349.1×10−31×vv=7.28×106Let potential difference be Δv12mv2=eΔv (e=charge on e−)12×9.1×10−31×52.99×10121.6×10−19=ΔvΔv=150Volts

What is the speed of an electron whose de Broglie wavelength is $0.1 n m$ ? By what potential difference, must have such an electron accelerated from an initial speed zero?