Question

1.) Calculate the wavelengths of the first five members of the Lyman series of spectral lines, providing the result in units Angstrom with percision one digit after the decimal point.

2.) Calculate the wave numbers of the first five members of the Pashen series. For the Rydberg constant, use the book value given in the text. (Rydberg constant =  109737.1cm^-1)

Answer 1

1) For the energy in the hydrogen atom where the initial energy corresponds to energy level n and the final energy corresponds to energy level m,

Where R is the same Rydberg constant for hydrogen from Rydberg's long known formula

1/lambda = R ( 1/m^2 - 1/n^2 )

The wavelengths (nm) in the Lyman series are all ultraviolet. where m = 1 for lyman series

n = 2 wavelength = 12.16 angstrom

n= 3 wavelength = 10.26 angstrom

n = 4 wavelength = 9.73 angstrom

n = 5 wavelength = 9.50 angstrom

n = 6 wavelength = 9.38 angstrom

2) For the paschen series m = 3

n= 4 wavenumber = 5.333 * 10 ^ -3 inverse angstrom

n = 5 wavenumber = 7.800 * 10^ -3 inverse angstrom

n = 6 wavenumber = 9.14 * 10^-3 inverse angstrom

n = 7 wavenumber = 9.95 * 10 ^-3 inverse angstrom

n = 8 wavenumber = 1.07 * 10^-3 inverse angstrom