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The wavelength Ha line is 6563 Å ....

The wavelength `H_a` line is 6563 Å . Calculate the wavelength of First member of Lyman series

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`(1 )/( lamda _a) = R_n [(1)/(2^2) -(1)/(3^2)]=R_B[1/4 -1/9 ] = (5R_H)/(36 )`
` therefore lamda_a = ( 36 )/( 5R_H) `…….(1)
(a) For lyman series `therefore (1)/( lamda_(IL ) ) = R_H [1/(I^2)-(1)/(2^2) ]= (3R_H )/(4 )`
` lamda _(IL ) =(4) /(3R_H)xx (5R_H)/(36 ) = (5)/(27 )`
` lamda _(IL ) =(5 )/(27 ) xx lamda _a = (5)/( 27 ) xx 6563 = 1215 Å`
(b ) for pachen series `, (1) /(lamda_(IP)) =R_H [(1)/(3^2)-(1)/(4^2)]= (7R_H)/(16xx 9)`
` lamda _(I P) = ( 16xx 9)/( 7 R_H) ...... (3)`
` therefore (lamda _(IP) )/(lamda_a) = ( 9xx 16 )/(7 R_H) xx (5R_H)/( 36 ) = (20)/(7)`
` lamda _(IP) = (20 )/(7) xx lamda _a ( 20xx6563 )/(7 ) = 18751 Å`
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