Question

$(a)r_{1}:r_{2}:r_{3} = 1^{2}:2^{2}:3^{2} = 1:4:9$

$(c)\lambda = \frac{c}{v} = \frac{3 \times 10^{8}}{6 \times 10^{14}} = 5 \times 10^{- 7}\text{ m = 500 nm}$

$(d)\lambda = \frac{h}{\sqrt{2mE}} \Rightarrow \lambda \propto \frac{1}{\sqrt{m}} $$$\therefore\lambda_{H}:\lambda_{H_{e}}:\lambda_{cn_{4}} = \frac{1}{\sqrt{1}}:\frac{1}{\sqrt{4}}:\frac{1}{\sqrt{16}} = 4:2:1$$