Physics -MC

[匿名]

2009-07-11 4:20 pm

An electron moving along the axies is described by a wavefunction Ψ (x). the uncertainty in position asscoiated with this wavefunction is 3 x 10^-9 m. If the velocityVx of the electron is measured in the state Ψ (x), a spread of results may be obtained. Estimate the minimun uncertainty associated with this velocity measurement. Choose from the key the one option that is closest to your estimate (whether larger or smaller)

A 10^6 m/s
B 10^5 m/s
C 10^4 m/s
D 10^0 m/s
E 10^-2 m/s
F 10^-4 m/s
G 10^-6 m/s
H There is no uncertainty associated with the velocity measurement

回答 (1)

Prof. Physics

2009-07-11 7:20 pm

✔ 最佳答案

By Heisenberg's uncertainty principle,

ΔxΔp >= h / 4π

Where

Δx is the uncertainty in position

Δp is the uncertainty in momentum of the electron

h is Planck constant, h = 6.63 X 10-34 Js

So,

(3 X 10-9)Δp >= (6.63 X 10-34) / 4π

Uncertainty in momentum, Δp >= 1.76 X 10-26 kgms-1

Mass of electron, m = 9.11 X 10-31 kg

So,

Uncertainty in velocity, Δv = 1.76 X 10-26 / 9.11 X 10-31

= 2.0 X 104 ms-1

The best answert is C.

參考: Physics king

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