Question

Consider the 1st emission line of the Lyman series of the H-atom and calculate its photon frequency with and without considering the finite mass of the proton. Calculate the frequency under the assumption of the proton being fixed in space (use me) and under the realistic assumption that the proton is mobile (use the reduced mass μ). Give the error in the approximate solution in terms of ppm compared to the exact solution.

Answer 1

E    

1st emission of Lyman series of H - atom , Change in energy is

                =        –(2.178 × 10^-18 J) ( 1/1² - 1/2²)

                  =        –1.6 * 10^-18 J

                                                          

R = 109677 cm–1

Z = 1 (for hydrogen atom) n1= 1,     n2= 2 (for 1st line in Lyman series)

=   109677 [ 1 / 1 - 1 / 4 ] = 109677 * .75

= 82257.75cm-1 or 1.215 * 10 ^-5 cm-1

Wavelength = 1 / 82257.75 = 1215 A⁰

Frequency v = c / = 3 * 10 ¹⁰ cm/s / 1.215 * 10 ^-5cm-1 = 2.46773 * 10¹⁵ s