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QPages 384-386: Q17: HC Verma: Concepts of Physics - Volume 2 Bohr's Model and Physics of the Atom Pages 384-386: Q17 Solution: A gas of hydrogen-like ions is prepared in a particular excited …

A gas of hydrogen-like ions is prepared in a particular excited state A. It emits photons having wavelength equal to the wavelength of the first line of the Lyman series together with photons of five other wavelengths. Identify the gas and find the principal quantum number of the state A.

Step-by-Step Verified Solution

**Answer:** The gas is Li__ (Z = 3), and the principal quantum number of state A is n = 4. **Step-by-Step Explanation:** The first line of Lyman series has wavelength corresponding to transition 2 _ 1. For a hydrogen-like ion, this wavelength is _ = 1240/(13.6 _ Z_ _ 3/4) = 121.6/Z_ nm. The gas emits this wavelength plus five other wavelengths. Total number of wavelengths from state n is n(n_1)/2 = 6, so n = 4. The ion must be Li__ (Z = 3) because its Lyman _ wavelength matches the given condition [citation:3].

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