Thursday, February 24, 2011

Mastering Physics: ± Simultaneous Measurements of Position and Velocity

Part A
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:
\Delta x \Delta p_x \ge \hbar,
where \Delta x is the uncertainty in the x coordinate of a particle, \Delta p_x is the particle's uncertainty in the x component of momentum, and \hbar = \frac{h}{2\pi}, where h is Planck's constant.
Express your answer in meters per second to three significant figures.
ANSWER:

  v_x  = 57.9
  \rm m/s


Part B
Repeat Part A for a proton.
Express your answer in meters per second to three significant figures.
ANSWER:

  v_x  = 3.16×10−2
  \rm m/s

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