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):}`

n_(1) value in Balmer series is

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 the" n^(th)"shell",(P),2(2l+1)),((B),"Maximum number of electrons in a subshell",(Q),n),((C),"Number of subshell in" n^(th)"shell",(R),2l+1),((D),"Number of orbitals in a subshell",(S),n^(2)):}

Find the sum to n terms of the series, whose n^(t h) terms is given by : (2n-1)^2

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.

Sum to n terms of the series :1 + 2 (1 + (1)/(n)) + 3 (1 + (1)/(n )) ^(2) + ………

The Lyman series of the hydrogen spectrum can be represented by the equation v = 3.2881 xx 10^(15)s^(-1)[(1)/((1)^(2)) - (1)/((n)^(2))] [where n = 2,3,…….) Calculate the maximum and minimum frequencies of the lines in this series

Excited atoms emit radiations consisting of only certain discrete frequencise or wavelengths. In spectroscopy it is often more convenient to use freuquencies and wave numbers are proportional ot energy and spectroscopy involves transitions between different energy levels . The line spectrum shown by a single electron excited atom (a finger print of an atom) can be given as 1/(lambda)=barvR_(H).Z^(2)[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))] where Z is atomic number of single electron atom and n_(1),n_(2) are integers and if n_(2)gt n_(1), then emission spectrum is noticed and if n_(2)ltn_(1), then absorption spectrum is noticed. Every line in spectrum can be represented as a difference of two terms (R_(H)Z^(2))/(n_(1)^(2)) "and"(R_(H)Z^(2))/(n_(2)^(2)). The ratio of wavelength for II line fo Balmer series and I line of Lyman series for H-like species is :

The sum of series Sigma_(n=1)^(oo) (2n)/(2n+1)! is

Find the sum of series upto n terms ((2n+1)/(2n-1))+3((2n+1)/(2n-1))^2+5((2n+1)/(2n-1))^3+...