Treat the hydrogen atom as a one-dimensional entity of length 2 a_{0} and determine the electron’s minimum kinetic energy.
Strategy We will use the uncertainty principle to determine K_{\min }. Equation (5.43) gives us the minimum kinetic energy for a particle known to be located within a distance \ell.
K_{\min }=\frac{p_{\min }^{2}}{2 m} \geq \frac{(\Delta p)^{2}}{2 m} \geq \frac{\hbar^{2}}{2 m \ell^{2}} (5.43)