If, in 1 / =Ry ( 1/ n21 1/ n22 ) you set n1 = 1 and take n2 greater than 1 , you

Question

If, in 1 / =Ry  ( 1/ n21 1/ n22 )

you set n1 = 1 and take n2 greater than 1 ,

you generate what is known as the Lyman series.

A) Find the wavelength of the ?rst member of this series.

The value of ¯ h is 1.05457 ×1034 J · s

The Rydberg constant for hydrogen is 1.09735 x10 m1

The Bohr radius is 5.29177 ×10 11 m

And the ground state energy for hydrogen is 13.6057 eV.

Answer in units of nm.

B) Consider the next three members of this series.

The wavelengths of successive members of the

Lyman series approach a common limit as n2 .

What is this limit?

Answer in units of nm.

Explanation / Answer

   1/   =   R *(1/n12   -   1/n22)    a.   For firstmember   n1   =   1,   n2   =   2    1/21   =   1.09735* 107 *(1/12   -   1/22)   =   8.23012* 106       =>   21   =   1/ 8.23012 *106    =   1.2150 *10-7   m   =   121.50   nm    b.   Secondmember,   n2   =   3       1/31   =   1.09735* 107 *(1/12   -   1/32)   =   9.75422* 106      =>   31   =   1/ 9.75422 *106    =  1.02520 *10-7   m   =   102.20   nm       Thirdmember   n2   =   4          1/41   =   1.09735* 107 *(1/12   -   1/42)   =   1.02876*107       =>   41   =   1/ 1.02876 *107    =   9.7204 *10-8  m   =   97.204   nm       For fourthmember,   n2   =   5    1/51   =   1.09735* 107 *(1/12   -   1/52)   =   1.05346* 107    =>   51   =   1/ 1.05346 *107   =   9.492 *10-8  m   =   94.92   nm    For serieslimit   n2   =       =>   limit   =  1.09735* 107 *(1/12   -   1/2)   =   1.09735* 107    =>   21   =   1/ 1.09735 *107    =   9.113 *10-7   m   =   91.13   nm    =>   31   =   1/ 9.75422 *106    =  1.02520 *10-7   m   =   102.20   nm       Thirdmember   n2   =   4          1/41   =   1.09735* 107 *(1/12   -   1/42)   =   1.02876*107       =>   41   =   1/ 1.02876 *107    =   9.7204 *10-8  m   =   97.204   nm       For fourthmember,   n2   =   5    1/51   =   1.09735* 107 *(1/12   -   1/52)   =   1.05346* 107    =>   51   =   1/ 1.05346 *107   =   9.492 *10-8  m   =   94.92   nm    For serieslimit   n2   =       =>   limit   =  1.09735* 107 *(1/12   -   1/2)   =   1.09735* 107    =>   21   =   1/ 1.09735 *107    =   9.113 *10-7   m   =   91.13   nm    =>   41   =   1/ 1.02876 *107    =   9.7204 *10-8  m   =   97.204   nm       For fourthmember,   n2   =   5    1/51   =   1.09735* 107 *(1/12   -   1/52)   =   1.05346* 107    =>   51   =   1/ 1.05346 *107   =   9.492 *10-8  m   =   94.92   nm    For serieslimit   n2   =       =>   limit   =  1.09735* 107 *(1/12   -   1/2)   =   1.09735* 107    =>   21   =   1/ 1.09735 *107    =   9.113 *10-7   m   =   91.13   nm    =>   51   =   1/ 1.05346 *107   =   9.492 *10-8  m   =   94.92   nm    For serieslimit   n2   =       =>   limit   =  1.09735* 107 *(1/12   -   1/2)   =   1.09735* 107    =>   21   =   1/ 1.09735 *107    =   9.113 *10-7   m   =   91.13   nm    =>   21   =   1/ 1.09735 *107    =   9.113 *10-7   m   =   91.13   nm    

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