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  4. Suggest two transitions in the atomic spectrum of hydrogen for which the wave number ratio is 108: 7

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Q. Suggest two transitions in the atomic spectrum of hydrogen for which the wave number ratio is $108 : 7$

Structure of Atom

Solution:

$\bar{v}=R_{ H }\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right)$

For first Lyman transition,

$\bar{v}=R_{ H }\left(\frac{1}{1^{2}}-\frac{1}{2^{2}}\right)=\frac{3}{4} R_{ H }$

For first Balmer transition,

$\bar{v}=R_{H}\left(\frac{1}{2^{2}}-\frac{1}{3^{2}}\right)=\frac{5}{36} R_{H}$

For first Paschen transition,

$\bar{v}=R_{ H }\left(\frac{1}{3^{2}}-\frac{1}{4^{2}}\right)=\frac{7}{144} R_{ H }$

For first Brackett transition,

$\bar{v}=R_{ H }\left(\frac{1}{4^{2}}-\frac{1}{5^{2}}\right)=\frac{9}{400} R_{ H }$

Lyman : Paschen $=\frac{3}{4}: \frac{7}{144}=3:$

$\frac{7}{36}=108: 7$