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The x coordinate of an electron is measured with an uncertainty of 0.200 mm. Wha

ID: 1495664 • Letter: T

Question

The x coordinate of an electron is measured with an uncertainty of 0.200 mm. What is v_x, the x component of the electron's velocity, if the minimum percentage uncertainty in a simultaneous measurement of v_x is 1.00 % ? Use the following expression for the uncertainty principle: deltax deltap_x greaterthanorequalto h/2, where delta x is the uncertainty in the x coordinate of a particle, deltap_x is the particle's uncertainty in the x component of momentum, and h is Planck's constant. Express your answer in meters per second to three significant figures.

Explanation / Answer

Heisenberg uncertainty principle: x px /2
x * mvx /2
vx /(2mx)
vx h/(4mx) where x = 0.200 mm

vx = 6.63x10^-34 /(4*3.14*9.1x10^-27*0.200x10^-3) =0.29 x 10^-4

velocity = 0.29 x 10^-4 * 3x10^8 m/s *1/100 =87 m/s..........Ans.