What is the ratio of wave number of first line (lowest energy line) of Balmer series of H atomic spectrum to first line of its Brackett series?
Select the correct option:
A
5 : 1
B
5 : 0.81
C
5 : 1.75
D
5 : 27
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$\overline{\mathrm{V}}_1=\mathrm{R}_{\mathrm{H}}(\mathrm{z})^2\left[\frac{1}{2^2}-\frac{1}{3^2}\right] \Rightarrow \mathrm{I}^{\mathrm{st}}$ line of Balmer series
$\overline{\mathrm{V}}_2=\mathrm{R}_{\mathrm{H}}(\mathrm{z})^2\left[\frac{1}{4^2}-\frac{1}{5^2}\right] \Rightarrow \mathrm{I}^{\mathrm{st}}$ line of Brackett series $\frac{\overline{\mathrm{V}}_1}{\overline{\mathrm{~V}}_2}=\frac{500}{81} \Rightarrow 5: 0.81$
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