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

For the Paschen series the value of n_(1) and n_(2) in the expression Delta E= Rhc ((1)/(n_(1)^(2))-(1)/(n_(2)^(2))) are

For a single electron atom or ion the wave number of radiation emitted during the transition of electron from a higher energy state (n = n_(2)) to a lower energy state (n=n_(1)) is given by the expression: bar(v) = (1)/(lambda) = R_(H).z^(2) ((1)/(n_(1)^(2))-(1)/(n_(2)^(2))) ...(1) where R_(H) = 2(pi^(2)mk^(2)e^(4))/(h^(3)c) = Rydberg constant for H-atom Where the terms have their usual meanings. Considering the nuclear motion, the most accurate expression would have been to replace mass of electron (m) by the reduced mass (mu) in the above expression, defined as mu = (m'.m)/(m'+m) where m'= mass of nucleus For Lyman series: n_(1) =1 (fixed for all the lines) while n_(2) = 2,3,4 ... for successive lines i.e. 1^(st), 2^(nd),3^(rd) ... lines, respectively. For Balmer series: n_(1) = 2 (fixed for all the lines) while n_(2) = 3,4,5 ... for successive lines. The ratio of the wave numbers for the highest energy transition of e^(-) in Lyman and Balmer series of H-atom is:

For a single electron atom or ion the wave number of radiation emitted during the transition of electron from a higher energy state (n = n_(2)) to a lower energy state (n=n_(1)) is given by the expression: bar(v) = (1)/(lambda) = R_(H).z^(2) ((1)/(n_(1)^(2))-(1)/(n_(2)^(2))) ...(1) where R_(H) = 2(pi^(2)mk^(2)e^(4))/(h^(3)c) = Rydberg constant for H-atom Where the terms have their usual meanings. Considering the nuclear motion, the most accurate expression would have been to replace mass of electron (m) by the reduced mass (mu) in the above expression, defined as mu = (m'.m)/(m'+m) where m'= mass of nucleus For Lyman series: n_(1) =1 (fixed for all the lines) while n_(2) = 2,3,4 ... for successive lines i.e. 1^(st), 2^(nd),3^(rd) ... lines, respectively. For Balmer series: n_(1) = 2 (fixed for all the lines) while n_(2) = 3,4,5 ... for successive lines. If proton in H-nucleus be replaced by positron having the same mass as that of electron but same charge as that of proton, then considering the nuclear motion, the wavenumber of the lowest energy transition of He^(+) ion in Lyman series will be equal to

The emission spectrum of hydrogen is found to satisfy the expression for the energy change Delta E (in joules) such that Delta E = 2.18 xx 10^(-18)((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))J where n_(1) = 1,2,3,.... and n_(2) = 2,3,4,... The spectral lines correspond to Paschen series if

The emission spectrum of hydrogen is found to satisfy the expression for the energy change Delta E (in joules) such that Delta E = 2.18 xx 10^(-18)((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))J where n_(1) = 1,2,3,.... and n_(2) = 2,3,4,... The spectral lines correspond to Paschen series if

The only electron in the hydrogen atom resides under ordinary conditions on the first orbit. When energy is supplied, the electron moves to higher energy orbit depending on the amount of energy absorbed. When this electron returns to any of the lower orbits, it emits energy. Lyman series is formed when the electron returns to the lowest orbit while Balmer series is formed when the electron returns to second orbit. Similarly, Paschen, Brackett and Pfund series are formed when electron returns to the third, fourth orbits from higher energy orbits respectively (as shown in figure) Maximum number of lines produced when an electron jumps from nth level to ground level is equal to (n(n-1))/(2) . For example, in the case of n = 4, number of lines produced is 6. (4 rarr 3, 4 rarr 2, 4 rarr 1, 3 rarr 2, 3 rarr 1, 2 rarr 1) . When an electron returns from n_(2) to n_(1) state, the number of lines in the spectrum will be equal to ((n_(2) - n_(1))(n_(2)-n_(1) +1))/(2) If the electron comes back from energy level having energy E_(2) to energy level having energy E_(2) then the difference may be expressed in terms of energy of photon as E_(2) - E_(1) = Delta E, lambda = (h c)/(Delta E) . Since h and c are constant, Delta E corresponds to definite energy, thus each transition from one energy level to another will prouce a higher of definite wavelength. THis is actually observed as a line in the spectrum of hydrogen atom. Wave number of the line is given by the formula bar(v) = RZ^(2)((1)/(n_(1)^(2)) - (1)/(n_(2)^(2))) Where R is a Rydberg constant (R = 1.1 xx 10^(7)) (i) First line of a series : it is called .line of logest wavelength. or .line of shortest energy.. (ii) Series limit of last of a series : It is the line of shortest wavelength or line of highest energy. The difference in the wavelength of the 2^(nd) line of Lyman series and last line of Bracket series in a hydrogen sample is

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 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 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):}