Answer to Question #94312 in Quantum Mechanics for Golrias

Question

The natural uncertainty in the measurement of speed of an electron in an atom is

estimated to be 2.2x10^4 m/s

Answer 1

We can apply Heisenberg uncertainty principle to find the natural uncertainty in the measurement of the particle's position:

$$∆x∆p\geq\frac{\hbar}{2},\\ \space\\ ∆x\geq\frac{\hbar}{2m_e∆v}=\frac{1.055\cdot10^{-34}}{2\cdot[9.109\cdot10^{-31}]\cdot[2.2\cdot10^{-34}]},\\ \space\\ ∆x\geq2.631\cdot10^{-9}\text{ m}.$$