Practicing Success
Calculate the uncertainty in the position of an electron if the uncertainty in its velocity is \(5.7 \text{ × }10^5ms{-1}\). |
\(\pm 10^{-8}m\) \(\pm 10^{-10}m\) \(\pm 10^{-12}m\) \(\pm 10^{-14}m\) |
\(\pm 10^{-10}m\) |
The correct answer is option 2. \(\pm 10^{-10}m\). Here, \(\Delta v\text{ = }5.7 \text{ × }10^5ms^{-1}\) \(m\text{ = 9.1}\text{ × }10^{-31}kg\) \(\Delta x\text{ = }\frac{h}{4\pi \text{ × }m\text{ × }\Delta v}\) \(\Delta x\text{ = }\frac{6.6\text{ × }10^{-34}kgm^2s^{-1}}{4\text{ × }\frac{22}{7}\text{ × }9.1\text{ × }10^{-31}kg\text{ × }5.7\text{ × }10^5ms{-1}}\) \(\Delta x\text{ = }1.0 \text{ × }10^{-10}m\) \(\text{i.e., Uncertainty in the position =}\pm 10^{-10}m\) |