Chemistry

Chemistry

Problem

Light of wavelength 97.3 nm97.3\,\text{nm} is observed in the hydrogen emission spectrum. If this line belongs to the Lyman series (nf=1n_f = 1), determine the principal quantum number nin_i of the initial state. Use RH=1.097×107 m−1R_H = 1.097 \times 10^{7}\,\text{m}^{-1}.
Intuitive explanation

The Rydberg formula connects the wavelength of emitted light to the quantum jumps an electron makes within an atom. Here, you're working backwards: given the wavelength and knowing the electron lands in nf=1n_f = 1 (Lyman series), you need to find which higher level it started from. Rearrange the Rydberg equation to isolate nin_i, then solve—the math is straightforward once you set it up correctly.

Intuitive explanation

The Rydberg formula connects the wavelength of emitted light to the quantum jumps an electron makes within an atom. Here, you're working backwards: given the wavelength and knowing the electron lands in nf=1n_f = 1 (Lyman series), you need to find which higher level it started from. Rearrange the Rydberg equation to isolate nin_i, then solve—the math is straightforward once you set it up correctly.

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