Numerical

Calculate the wavelength of an electron moving with a velocity of 2.05 × 10^{7} ms^{-1}.

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#### Solution

According to de Broglie’s equation,

`lambda = "h"/("mv")`

λ = wavelength of moving particle

m = mass of particle

v = velocity of particle

h = Planck’s constant

Substituting the values in the expression of λ:

`lambda = (6.626 xx 10^(-34) "Js")/((9.10939xx10^(-31) "kg")(2.05xx10^7 "ms"^(-1)))`

`lambda = 3.548 xx 10^(-11) " m"`

Hence, the wavelength of the electron moving with a velocity of 2.05 × 10^{7} ms^{–1} is 3.548 × 10^{–11} m.

Concept: Towards Quantum Mechanical Model of the Atom - Dual Behaviour of Matter

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