Correct Answer - `n=4; 18750Å; 6547Å`
Total energy of gaseous hydrogen
`=(12.9-13.6)eV=-0.7eV`
`:. -13.6/(n^(2))=-0.7, n^(2)=13.6/0.7 =19.4`
`n=sqrt(19.5)lt5`
`:. n=4`
for the first member of Paschen series,
`E=E_(4)-E_(3)=-13.6/(4^(2))-(-13.6/(3^(2)))`
`=-0.85+1.51=0.66eV`
`(hc)/lambda=0.66xx1.6xx10^(-19)J`
`lambda=(hc)/(0.66xx1.6xx10^(-19))m`
`=(6.6xx10^(-34)xx3xx10^(8)xx10^(10)Å)/(0.66xx1.6+10^(-19))`
`=18750Å`
and for first member of Balmer series
`E=E_(3)-E_(2)=-13.6/(3^(2))-(-13.6/(2^(2)))ev`
`=-1.51+3.4=1.89ev`
`(hc)/lambda=1.89xx1.6xx10^(-19)J`
`lambda=(hc)/(1.89xx1.6xx10^(-19))`
`=(6.6xx10^(-34)xx3xx10^(8))/(1.89xx1.6xx10^(-19))m`
`=6.5476xx10^(-7)m=6547Å`