Physics20815 marksNumerical: uncertainty principle calculationUncertainty principle and its origin
A small particle of mass 10-6 g moves along the x axis; its speed is uncertain by 10-6 m/sec. (a) What is the uncertainty in the x coordinate of the particle? (b) Repeat the calculation for an electron assuming that the uncertainty in its velocity is also 10-6 m/sec.
A small particle of mass $10^{-6}$ g moves along the x axis; its speed is uncertain by $10^{-6}$ m/sec. (a) What is the uncertainty in the x coordinate of the particle? (b) Repeat the calculation for an electron assuming that the uncertainty in its velocity is also $10^{-6}$ m/sec. [5]
- Mass of small particle: $m = 10^{-6}$ g $= 10^{-6} \times 10^{-3}$ kg $= 10^{-9}$ kg - Uncertainty in speed: $\Delta vx = 10^{-6}$ m/s - Mass of electron: $me = 9.11 \times 10^{-31}$ kg - Planck's constant: $h = 6.626 \times 10^{-34}$ J·s The uncertainty principle: $$\Delta x \cdot \Delta px \g...