Question

If uncertainties in the measurement of position and momentum of an electron are equal, the uncertainty in the measurement of velocity is

• A. $8.0\times {10}^{12}m{s}^{-1}$
• B. $4.2\times {10}^{10}m{s}^{-1}$
• C. $8.5\times {10}^{10}m{s}^{-1}$
• D. $6.2\times {10}^{10}m{s}^{-1}$

Answer 1

Answer: (A)

Given, $\Delta x=\Delta P$ or $\Delta x=m\cdot \Delta v$ From Heisenbergs uncertainty principle, $\Delta x\cdot m\cdot \Delta v=\frac{h}{4\pi }$ $\Rightarrow$ $m\cdot \Delta v\cdot m\Delta v=\frac{h}{4\pi }$ ${(\Delta v)}^2=\frac{h}{4\pi m^2}$ $\Rightarrow$ $\Delta v=\frac{1}{2m}\sqrt{\frac{h}{\pi }}$ $=\frac{1}{2\times 9.1\times {10}^{-31}}\sqrt{\frac{6.63\times {10}^{-34}}{3.14}}$ $=7.98\times {10}^{12}m{s}^{-1}$ $=8\times {10}^{12}m{s}^{-1}$