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Question
The mass of an electron is 9.1 × 10–31 kg. If its K.E. is 3.0 × 10–25 J, calculate its wavelength.
Solution
From de Broglie’s equation,
`lambda = "h"/("mv")`
Given,
Kinetic energy (K.E) of the electron = 3.0 × 10-25 J
Since `"K.E" = 1/2 "mv"^2`
:. Velocity (v) = `sqrt((2"K.E")/"m")`
`= sqrt((2(3.0xx10^(-25) " J"))/(9.10939 xx10^(-31)))`
`= sqrt(6.5866xx10^4)`
`v = 811.579 " ms"^(-1)`
Substituting the value in the expression of λ:
`lambda = (6.626 xx 10^(-34) " Js")/((9.10939xx10^(-31) " kg")(811.579 " ms"^(-1)))`
`lambda = 8.9625 xx 10^(-7) " m"`
Hence, the wavelength of the electron is 8.9625 × 10–7 m.
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