Modern Physics: Mastering Physics: ± Simultaneous Measurements of Position and Velocity

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 . What is , the x component of the electron's velocity, if the minimum percentage uncertainty in a simultaneous measurement of 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.

Part A

The x coordinate of an electron is measured with an uncertainty of 0.200

. What is

, 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: