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Question
Calculate the wavelength associated with an electron, its momentum and speed when it is moving with the kinetic energy of 150 eV.
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Solution
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
As KE ∝ `sqrt"V"`, we get
`"v'"/"v" = sqrt(150/54)` = 1.666
∴ v' = 1.666 v = (1.666)(4.359 × 106)
= 7.262 × 106 m/s
This is the speed of the electron.
p' = mv' = (9.1 × 10-31)(7.262 × 106)
= 6.608 × 10-24 kg.m/s
`lambda' = "h"/"p'" = (6.63 xx 10^-34)/(6.608 xx 10^-24) = 1.003 xx 10^-10`m
= 1.003 Å = 0.1003 nm
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