Chapter 90 of 2363 min read

Bohr model and hydrogen spectrum

Why this is asked: Bohr's energy and radius formulas are exact only for one-electron species (H, He⁺, Li²⁺) — applying them to a multi-electron atom without adjustment is the usual overreach. Only the Balmer series (transitions down to n=2) falls in the visible range; Lyman is UV and the rest are infrared.

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Test yourself

•The energy and radius of the first Bohr orbit of $H e^{+}$ and $L i^{2 +}$ are (given $R_{H} = 2.18 \times 1 0^{- 18}$ J, $a_{0} = 52.9$ pm):
•The ratio of the wavelengths of the light absorbed by a hydrogen atom when it undergoes the $n = 2 \to n = 3$ and $n = 4 \to n = 6$ transitions, respectively, is:
•The energy of an electron in the ground state ( $n = 1$ ) of the $H e^{+}$ ion is $- x$ J. Then that of an electron in the $n = 2$ state of the $B e^{3 +}$ ion, in J, is:

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