The equivalent wavelength of a moving electron has the same value as that of a photon of energy 6 × 10^{–17} J. Calculate the momentum of the electron.

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#### Solution

According to the de Broglie hypothesis, the momentum of an electron is given by

p=6.626×10−343.31×10−9" data-mce-style="position: relative;">p=h/λp=6.626×10−343.31×10−9

whereh = Planck's constant=6.626×10^{−34}

λ = Wavelength of electron

Energy of photon, E=hc/λ=6×10^{−17} J

where c = Speed of light=3×10^{8} m/s

λ= Wavelength of photon

`∴ λ=(hc)/E`

`⇒λ=((6.626xx10−34)(3xx108 ))/(6xx10−17)`

`⇒λ=3.31xx10^−9 m`

From p=h/λ,

we have

`p=(6.626xx10^−34)/(3.31×10^−9)`

`⇒p=2×10−25 kg m s^−1`

Concept: Heisenberg and De Broglie Hypothesis

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