Answer to Question #208736 in Quantum Mechanics for Bennie

Question

A typical atomic nucleus is about 5.0 × 10−15𝑚 in radius. Use the

uncertainty principle to place a lower limit on the energy an electron must

have if it is to be part of a nucleus.[ans; 3.3 × 10−12𝐽]

II. A hydrogen atom is 5.3 × 10−11𝑚 in radius. Use the uncertainty principle

Answer 1

$p=\frac{h}{4\pi r}=2.11\cdot 10^{-20}~\frac{kg\cdot m}{s},$

$E=c\sqrt{p^2+m^2c^2}\approx 3.3\cdot 10^{-12}~J.$