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Question
Show that if the measurement of the uncertainty in the location of the particle is equal to its de Broglie wavelength, the minimum uncertainty in its velocity (ΔV) is equal to 1/4π of its velocity (V).
Solution
`∆"x".∆"p" ≥ "h"/(4π)`
`λ.("m"∆"v") ≥ "h"/(4π)`
∆v `≥ "h"/(4π("m"λ))`
∆v `≥ "h"/(4π xx "m" xx "h"/"mv")` .........[∵ λ = "h"/"mv"]
∆v `≥ "v"/(4π)`
Therefore, minimum uncertainty in velocity = `"v"/(4π)`
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