Calculate the longest wavelength of radiation for the Paschen Series. (Answer: 1875 nm) 



Data Given:


Paschen Series:

∴ Rydberg constant = R = 1.097 ｘ 10⁷ m⁻¹


To Find:

Longest Wavelength = λmax =  ?



Solution:

Rydberg formula for Paschen Series:

1λ = R(  --------(1)

where n = 4,5,6,7,..............


For the longest Wavelength, the number of orbital n = 4 is used (ie. the electron jumps from orbital 4 to orbital no. 3)


Putting values in eqn (1)


\frac {1}{λ_{max}} = 1.097 ｘ 10⁻⁷ m⁻¹ (\ frac {1}{3²} - frac {1}{4²})


\frac {1}{λ_{max}} = 1.097 ｘ 10⁻⁷ m⁻¹ (\ frac {1}{9} - frac {1}{16})


\frac {1}{λ_{max}}= 1.097 ｘ 10⁻⁷ m⁻¹ (\ frac {16 - 9}{144})


\frac {1}{λ_{max}} = 1.097 ｘ 10⁻⁷ m⁻¹ (\ frac {7}{144})


\frac {1}{λ_{max}} = (\ frac {7.679 ｘ 10⁻⁷ m⁻¹}{144})


by flipping the fraction on both sides of the equation we get


\λ_{max} = \ frac {144}{7.679 ｘ 10⁻⁷ m⁻¹}


or


\λ_{max}  = 18.752 ｘ 10⁷ m


or


\λ_{max} = 1875.2 ｘ 10⁹ m


\λ_{max}  = 1875 nm ---------------Ans.


If expressing in Angstrom)
\λ_{min} = 18752 ｘ 10¹⁰ m
\λ_{min} = 18752 A°


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