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Question
An electron is accelerated from rest through a potential difference of 100 V. Find:
- the wavelength associated with
- the momentum and
- the velocity required by the electron.
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Solution
(i) Wavelength = λ = `"h"/sqrt(2 "meV")`
λ = `(6.6 xx 10^-34)/sqrt(2 xx 9.1 xx 10^-31 xx 1.6 xx 10^-19 xx 100)`
= 1.2 × 10−10 m
∴ λ = 1.2 Å
(ii) Momentum = p = `"h"/λ`
p = `(6.6 xx 10^-34)/(1.2 xx 10^-10)`
∴ p = 5.5 × 10−24 kg m/s
(iii) Momentum = p = mv
∴ Velocity = v = `"p"/"m"`
= `(5.5 xx 10^-24)/(9.1 xx 10^-31)`
= 6 × 106 m/s
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