The x coordinate of an electron is measured with an uncertainty of 0.200 m m . W

Question

The x coordinate of an electron is measured with an uncertainty of 0.200mm . What is vx, the x component of the electron's velocity, if the minimum percentage uncertainty in a simultaneous measurement of vx is 1.00% ? Use the following expression for the uncertainty principle:

(delta x)(deltapx) greater than or equal to h0,

where delta x is the uncertainty in the x coordinate of a particle, delta px is the particle's uncertainty in thexcomponent of momentum, and h0=h/(2pi), where h is Planck's constant.

Explanation / Answer

Planck's constant h = 6.626 * 10-34 m2kg/s
delta x = 0.200mm = 0.200 * 10-3 m The mass of electron m = 9.1 * 10-31 kg delta px = m delta vx = mvx * 1.0% = mvx / 100 As delta x delta px = delta x mvx / 100
delta x delta px = m [delta x vx / 100] > h / 2 pi
vx > 100 h / 2 Pi m delta x
= (100 * 6.626 * 10-34 m2kg/s) / (2 pi * 9.1 * 10-31 kg * 0.200 * 10-3 m)
= 57.9 m/s

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