All Problems Wave Properties of particles. Schrodinger Equation.
Problem 6.54
Calculate the most probable de Broglie wavelength of hydrogen molecules being in thermodynamic equilibrium at room temperature.
\(6.54 .\) First, let us find the distribution of molecules over de (\lambda) \(d \lambda\) where Broglie wavelengths. From the relation \(f(v) d v=-\varphi\) \(f(v)\) is Maxwell's distribution of velocities, we obtain \[ \varphi(\lambda)=A \lambda^{-4} \mathrm{e}^{-a / \lambda 2}, \quad a=2 \pi^{2} \hbar^{2} / n k T \] The condition \(d \varphi / d \lambda=0\) provides \(\lambda_{p r}=\pi \hbar / \sqrt{m k T}=0.09 \mathrm{nm}\)