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Question
Calculate the uncertainty in position of an electron, if Δv = 0.1% and υ = 2.2 × 106 ms-1
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Solution
Mass of an electron = m = 9.1 × 10-31 kg.
∆v = Uncertainty in velocity = `0.1/100` × 2.2 × 103 ms-1
∆υ = 0.22 × 104 = 2.2 × 103 ms-1
∆x . ∆υ . m = `"h"/(4π)`
∆x = `"h"/(∆"υ" . "m". 4π)`
= `(6.626 xx 10^-34)/(2.2 xx 10^3 xx 9.1 xx 10^-31 xx 4 xx 3.14)`
= `(6.626 xx 10^-34 xx 10^3 xx 10^31)/(2.2 xx 9.1 xx 4 xx 3.14)`
= `(6.626 xx 10^-6)/(251.45)`
= 0.02635 × 10-6
∆x = 2.635 × 10-8
Uncertainty in position = 2.635 × 10-8
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