In case of hydrogen spectrum wave number is given by
`barv=R_(H)[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))]` where `n_(1)gtn_(2)`
`{:(,"ColumnI",,"ColumnII"),((A),"Lyman series",(P),n_(2)=2),((B),"Balmer series",(Q),n_(2)=3),((C),"Pfund series",(R),n_(2)=6),((D),"Brackett series",(S),n_(2)=5):}`

In hydrogen spectrum wave number of different lines is given by 1/lambda=R_(H)[1/n_(i)^(2)-1/n_(f)^(2)] where R_(H)=1.090678xx10^(7)m^(-1) The wavelength of first line of Lyman series would be

For the Paschen series thr values of n_(1) and n_(2) in the expression Delta E = R_(H)c [(1)/(n_(1)^(2))-(1)/(n_(2)^(2))] are

{:(,"ColumnI",,"ColumnII"),((A),"Number of orbitials in then" n^(th)"sheel",(P),2(2l+1)),((B),"Maximum number of electrons in a subshell",(Q),n),((C),"Number of subshell in" n^(th)"sheel",(R),2l+1),((D),"Number of orbitals in a subshell",(S),n^(2)):}

For balmer series in the spectrum of atomic hydrogen the wave number of each line is given by bar(V)=R_(H)(1)/(n_(1)^(2))-(1)/(n_(2)^(2)) where R_(H) is a constant and n_(1) and n_(2) are integers which of the following statement (S) is / are correct 1 as wavelength decreases the lines in the series converge 2 The integer n_(1) is equal to 2 3 The ionization energy of hydrogen can be calculated from the wave number of these lines 4 The line of longest wavelength corresponds to n_(2)=3

For balmer series in the spectrum of atomic hydrogen the wave number of each line is given by bar(V) = R[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))] where R_(H) is a constant and n_(1) and n_(2) are integers. Which of the following statements (s), is (are correct) 1. As wave length decreases the lines in the series converge 2. The integer n_(1) is equal to 2. 3. The ionisation energy of hydrogen can be calculated from the wave numbers of three lines. 4. The line of shortest wavelength corresponds to = 3.

The sum of the series sum_(r=0)^(n)(-1)^(r)(n+2r)^(2) (where n is even) is equal to