Physics20755 marksNumerical: uncertainty principle positionUncertainty principle and its origin
A small particle of mass 10-6 gm moves along the x axis; its speed is uncertain by 105 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 105 m/sec. use the known values for electron
A small particle of mass $10^{-6}$ gm moves along the x axis; its speed is uncertain by $10^5$ 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 $10^5$ m/sec. use the known values for electrons and Planck's constant. [5]
- Mass of small particle: $m = 10^{-6}$ g $= 10^{-9}$ kg - Uncertainty in speed: $\Delta vx = 10^5$ 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: $$\Delta x \cdot \Delta px \geq \frac{h}{4\pi}$$ With