"calculation of the value of the first ionization energy from spectral data which gives the wavelength or frequency of the convergence limit."

 

Calculate the first ionization energy, in kJ mol−1 for hydrogen given that its shortest wavelength line in the Lyman series is 91.16 nm. h= 10-34 m2 kg / s J s; c = 2.998 x 108   m s -1; N A = 6.022 X 1023  mol−1.

 

The shortest wavelength in the lyman series corresponds to a transition of n = ∞ to n =  1

 

IE1 = hv = hc/ λ

 

IE1= 6.626 x 10 -34  J s x 2.998 x 108  m s -1

                               91.16 x 10-9 m

 

EXPRESSED IN kJ mol-1

 

IE1= (2.179 X 10 -18 J ) x (6.022 x 1023 mol -1) = 1.312 x 10 6 J mol -1

 

= 1312 kJ mol -1