For a non-relativistic particle, the ratio of phase velocity to group velocity of de Broglie waves is:

Correct option is A

​$$\begin{aligned}&\text{For a non-relativistic particle, the \textbf{group velocity} } v_g \text{ corresponds to the particle velocity } v: \\&v_g = v \\&\text{The \textbf{phase velocity} } v_p \text{ of the de Broglie wave is given by:} \\&v_p = \frac{E}{p} \\&\text{where } E \text{ is kinetic energy and } p \text{ is momentum.} \\&\text{For a non-relativistic particle:} \\&E = \frac{1}{2} mv^2, \quad p = mv \\&\text{So,} \\&v_p = \frac{E}{p} = \frac{\frac{1}{2} mv^2}{mv} = \frac{v}{2} \\&\text{Therefore,} \\&\frac{v_p}{v_g} = \frac{v/2}{v} = \frac{1}{2} \\&\text{So the ratio } v_p : v_g = 1 : 2.\end{aligned}$$​​