The wavelength of first Lyman lines of Hydrogen (H), and ions are , and respectively. The ratio is

Question

The wavelength of first Lyman lines of Hydrogen (H), $H e^{+}$ and $L i^{2 +}$ ions are $λ_{1}$ , $λ_{2}$ and $λ_{3}$ respectively. The ratio $λ_{1} : λ_{2} : λ_{3}$ is ______

Smart Achievers · Accepted Answer

(3)

$\frac{1}{λ} \propto R_{n} Z^{2} \Rightarrow λ_{1} : λ_{2} : λ_{3} = \frac{1}{1^{2}} : \frac{1}{2^{2}} : \frac{1}{3^{2}} = 1 : \frac{1}{4} : \frac{1}{9} = 36 : 9 : 4$

Solution

Q.
The wavelength of first Lyman lines of Hydrogen (H), $H e^{+}$ and $L i^{2 +}$ ions are $λ_{1}$ , $λ_{2}$ and $λ_{3}$ respectively. The ratio $λ_{1} : λ_{2} : λ_{3}$ is ______

1 1 : 4 : 9

2 9 : 4 : 1

3 36 : 9 : 4

4 6 : 3 : 2

Ans.
(3)

$\frac{1}{λ} \propto R_{n} Z^{2} \Rightarrow λ_{1} : λ_{2} : λ_{3} = \frac{1}{1^{2}} : \frac{1}{2^{2}} : \frac{1}{3^{2}} = 1 : \frac{1}{4} : \frac{1}{9} = 36 : 9 : 4$

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