What is the calculated value if we replace m e in equation 1.25 by reduced mass?

Question

What is the calculated value if we replace mein equation 1.25 by reduced mass? compare your answer with experimental result, 109677.6 cm^-1 for rydberg constant. Equation 1.25 is Rinfinity below.

ce in a nalu at are excited to higIU, excited electrons fall back into WIL he theoretical formula (Equation 1.23) in the f y writing hv = hc: 3) in the form - 6 ) ations 1.11 and 1.24, we conclude that m e4 R. = 8e ch® ne Rydberg constant, Equation 1.11. of the physical constants given inside the front -

Explanation / Answer

* mass of electron is =9.1*10-31kg .

*rydberg equation is applicable on hydrogen atom or hydrogen like atoms only.

reduced mass of electron is given as =MN m/ MN+m where Mn is mass of nucleus of hydrogen and m is mass of electron.

*hydrogen has three isotopes having different masses of nucleus. i m here considering only 1H1because it is found in > 99.9 % in nature.

*calculation of reduced mass of electron= 1.627*10-27 kg(mass of nucleus of hydrogen)*9.1*10-31 kg(mass of e)/ 1.627 *10-27 +9.1*10-31 = 9.13*10-31 kg

*so you can see reduced mass and rest mass of electron are nearly same so if we replace rest ,mass of electron by reduced mass then value of rydberg constant will same

*R = me e4 / 8 epsilon 2 c h3 = 109677.7 cm-1 and nswer willbe same is we replace me with reducend mass of electron.

*comment for any misconception

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