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(A) The energy of the ground state of a hydrogen atom is $E_1 = -13.6 \ eV$. When an electron beam of $12.75 \ eV$ bombards the hydrogen gas,the energ

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either Paschen,Lyman or Balmer series

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(A) The energy of the ground state of a hydrogen atom is $E_1 = -13.6 \ eV$. When an electron beam of $12.75 \ eV$ bombards the hydrogen gas,the energy of the excited hydrogen atom becomes $E = -13.6 + 12.75 = -0.85 \ eV$. Using the formula $E_n = -13.6 / n^2 \ eV$,we find that $-0.85 = -13.6 / n^2$,which gives $n^2 = 16$,so $n = 4$. The possible transitions from the $n = 4$ state are: $n = 4$ $\rightarrow 3, 4$ $\rightarrow 2, 4$ $\rightarrow 1, 3$ $\rightarrow 2, 3$ $\rightarrow 1, 2$ $\rightarrow 1$. Transitions ending at $n = 1$ belong to the Lyman series $(4$ $\rightarrow 1, 3$ $\rightarrow 1, 2$ $\rightarrow 1)$. Transitions ending at $n = 2$ belong to the Balmer series $(4$ $\rightarrow 2, 3$ $\rightarrow 2)$. Transition ending at $n = 3$ belongs to the Paschen series $(4 \rightarrow 3)$. Thus,the emitted wavelengths belong to the Lyman,Balmer,and Paschen series.

$A$ $12.75 \ eV$ electron beam is used to bombard gaseous hydrogen at room temperature. The wavelengths emitted belong to which of the following series?

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