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(B) The $5^{th}$ excited state of a hydrogen atom corresponds to the principal quantum number $n = 6$. The ground state corresponds to $n = 1$. The Ba

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$4$

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(B) The $5^{th}$ excited state of a hydrogen atom corresponds to the principal quantum number $n = 6$. The ground state corresponds to $n = 1$. The Balmer series consists of spectral lines produced when an electron transitions from any higher energy level $(n_2 > 2)$ to the $n_1 = 2$ energy level. Given the electron transitions from $n = 6$ to $n = 1$,the transitions that result in the Balmer series are those ending at $n = 2$. These transitions are: $6 	o 2$,$5 	o 2$,$4 	o 2$,and $3 	o 2$. Thus,the total number of different spectral lines in the Balmer series is $4$.

The number of maximum possible different spectral lines obtained in the Balmer series,when an electron makes a transition to the ground state from the $5^{th}$ excited state in a sample of hydrogen atoms,is:

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