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Question
De Broglie proposed the wave nature of electrons suggesting matter waves.
Find the momentum, speed and De-Broglie wavelength of an electron with Kinetic energy of 120eV.
Find the momentum, speed and De-Broglie wavelength of an electron with Kinetic energy of 120eV.
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Solution
Here , E=120eV=120×1.6×10−19J , me=9.1×10−31kg , h=6,6×10−34JsNow , if v be the speed of electron , then E=1/2mev2or v=√2E/meor v=√2×120×1.6×10−19/9.1×10−31
or v=6.49×106m/s Now , momentum of electron, p=mev=9.1×10−31×6.49×106=5.9×10−24kgm/sde-Broglie wavelength of the electron, λ=h/p=6.6×10−34/5.9×10−24=1.1×10−10m
Now , if v be the speed of electron , then
E=1/2mev2
or v=√2E/me
or v=√2×120×1.6×10−19/9.1×10−31
or v=6.49×106m/s
Now , momentum of electron,
p=mev=9.1×10−31×6.49×106=5.9×10−24kgm/s
de-Broglie wavelength of the electron,
λ=h/p=6.6×10−34/5.9×10−24=1.1×10−10m
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