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प्रश्न
Calculate the wavelength associated with an electron, its momentum and speed when it is accelerated through a potential of 54 V.
उत्तर
Data: V = 54 V, m = 9.1 x 10-31 kg, e = 1.6 x 10-19C, h = 6.63 x 10-34 J.s, KE = 150 eV
We assume that the electron is initially at rest.
∴ Ve = `1/2 "mv"^2`
∴ v = `sqrt((2"Ve")/"m") = sqrt((2(54)(1.6 xx 10^-19))/(9.1 xx 10^-31))`
`= sqrt(19 xx 10^12)` = 4.359 × 106 m/s
This is the speed of the electron.
p = mv = (9.1 × 10-31)(4.359 × 106)
= 3.967 × 10-24 kg.m/s
This is the momentum of the electron. The wavelength associated with the electron,
λ = `"h"/"p" = (6.63 xx 10^-34)/(3.967 xx 10^-24) = 1.671 xx 10^-10`m
= 1.671 Å = 0.1671 nm
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