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Question
An electron is accelerated through a potential difference of 64 volts. What is the de-Broglie wavelength associated with it? To which part of the electromagnetic spectrum does this value of wavelength correspond?
Solution
de -Broglie wavelength,`lambda = h/(sqrt(2meV))`
Where,
`m ->\text { Mass of electron} = 9.1 xx 10^-31kg`
`lambda = (6.626 xx 10^-34)/(sqrt (2 xx 9.1 xx 10^-31 xx 1.6 xx 10^-19 xx 64))`
`lambda = (6.626 xx 10^-34)/(sqrt 1863.63, xx 10^-50)`
`lambda = (6.626 xx 10^-34)/(sqrt 1063.68 xx 10^-25)`
`=6.626/43.17 xx 10^-9`
`=0.15 xx 10^-9 m`
` =1.5 xx 10^-10 m`
This value of wavelength corresponds to the X-ray region of the electromagnetic spectrum.
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