What is the maximum number of emission lines when the excited electron of a H atom in n = 6 drops to the ground state?

Solution

Number of lines produced when electron from nth shell drops to the ground state

equals space fraction numerator straight n left parenthesis straight n minus 1 right parenthesis over denominator 2 end fraction space equals space fraction numerator 6 left parenthesis 6 minus 1 right parenthesis over denominator 2 end fraction space equals space 15

There 15 lines are produced because of the following transition:

space open table row cell 6 space rightwards arrow space 5 end cell row cell 6 space rightwards arrow 4 end cell row cell 6 space rightwards arrow 3 end cell row cell 6 space rightwards arrow 2 end cell row cell 6 space rightwards arrow 1 end cell end table close curly brackets space 5 space lines space space space space space open table row cell 5 space rightwards arrow space 4 end cell row cell 5 space rightwards arrow 3 end cell row cell 5 space rightwards arrow 2 end cell row cell 5 space rightwards arrow 1 end cell end table close curly brackets space space 4 space lines space space open table row cell 4 space rightwards arrow space 2 end cell row cell 4 space rightwards arrow 2 end cell row cell 4 space rightwards arrow 1 end cell end table close curly brackets space 3 space lines

open table attributes columnalign right end attributes row cell 3 space rightwards arrow space 2 end cell row cell 3 space space rightwards arrow 1 end cell end table close curly brackets space 2 space lines space space space open table row cell 2 rightwards arrow space 1 end cell end table close curly brackets space 1 space line Total space lines space space equals space 5 plus 4 plus 3 plus 2 plus 1 space equals space 15 space lines

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