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Question

When an electron is excited to $$n ^ { \text { th } }$$ energy state in hydrogen, the possible number of spectral lines emitted are


A
n
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B
2n
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C
n2n2
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D
n2+n2
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Solution

The correct option is C $$\dfrac { n ^ { 2 } - n } { 2 }$$
The number of energy states below with level =$$n-1$$
Total number of spectral  lines= sum of the volume of each energy state.
Hence, Total spectral lines=$$1+2+3+............n-1$$
$$ = \frac{{\left( {n - 1} \right)n}}{2} = \frac{{{n^2} - n}}{2}$$

Physics

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