Question

When an electron of an excited hydrogen atom descends, from an initial energy level (ni) to a lower (nf), characteristic electromagnetic radiation is emitted. The Bohr model of the H-atom allows the calculation of ?E for any pair of energy levels. ?E is related to the wavelength (?) of the radiation according to Einstein's equation ( ?E = [(hc)/?]). Distinct series of spectral lines have been classified according to nf: Lyman series:nf=1 (91<?<123 nm; near-UV). Balmer series:nf=2 (365<?<658 nm; visible). Paschen series:nf=3 (819<?<1877 nm; near-IR). Brackett series:nf=4 (1.456<?<4.054 ?m; short-to-mid-?-IR) One of the lines in the emission spectrum of the hydrogen atom has a wavelength of ? = 1876 nm. Identify the value of ninitial. Identify the value of nfinal .

Answer 1

--> Given the wavelength emitted = 1876 nm

1/wavelength = RZ² (1/nf² - 1/ni² ) { R= 1.09737×10⁷ m^?1 }

1/(1876*10^-9) = 1.09737×10⁷ m^?1 (1/nf² - 1/ni² )

(1/nf² - 1/ni² ) = 0.0486

here if you put nf = 3 and ni = 4 then you will get this. it is an hit and trial method.

so transition is fron n=4 to n=3.

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