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Question
An electron is accelerated through a potential difference of 81 V. What is the de Broglie wavelength associated with it? To which part of the electromagnetic spectrum does this wavelength correspond?
Solution
de-Broglie wavelength of an electron beam accelerated through a potential difference of V volts is
λ = `"h"/sqrt(2"meV") = 1.23/sqrt"V"` nm
V = 81 V, so λ = `1.23/sqrt81 xx 10^-9` m
λ = 1.36 Å
X-ray is the part of the electromagnetic spectrum does this wavelength corresponds. X-ray has wavelengths ranging from about 108 to 10−12 m.
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