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Question
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.
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Solution
(a) If the atom is excited to the principal quantum (n), then the number of transitions is given by
`(n(n-1))/2`
It is given that a total of 6 photons are emitted. Therefore, total number of transitions is 6.
`therefore (n(n-1))/2`
= 6
⇒ n = 4
Thus, the principal quantum number is 4 and the gas is in the 4th excited state.
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