The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series.
(R = Rydberg constant) [2026]

Question

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(4)

$Balmer series line \Rightarrow \bar{ν} = R_{H} Z^{2} [\frac{1}{2^{2}} - \frac{1}{n^{2}}]$

$if n = 3 \Rightarrow \bar{ν} = R {(1)}^{2} [\frac{1}{2^{2}} - \frac{1}{3^{2}}] = \frac{5 R}{36}$

$if n = 4 \Rightarrow \bar{ν} = \frac{3 R}{16}$

$if n = 5 \Rightarrow \bar{ν} = \frac{21 R}{100}$

Solution

Q.
The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series.
(R = Rydberg constant) [2026]

1 $\frac{7 R}{144}, \frac{3 R}{16}, \frac{16 R}{255}$

2 $\frac{5 R}{36}, \frac{8 R}{9}, \frac{15 R}{16}$

3 $\frac{3 R}{4}, \frac{3 R}{16}, \frac{7 R}{144}$

4 $\frac{5 R}{36}, \frac{3 R}{16}, \frac{21 R}{100}$

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Solution

Q. The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series. (R = Rydberg constant) [2026]

1 7R144, 3R16, 16R255

2 5R36, 8R9, 15R16

3 3R4, 3R16, 7R144

4 5R36, 3R16, 21R100