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(B) The potential energy $U$ of an electron in a hydrogen atom at a state $n$ is given by $U_n = -27.2 / n^2 \ eV$.For the first excited state $(n = 2

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$6.8 eV$

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(B) The potential energy $U$ of an electron in a hydrogen atom at a state $n$ is given by $U_n = -27.2 / n^2 \ eV$.For the first excited state $(n = 2)$, the potential energy is $U_2 = -27.2 / 2^2 = -6.8 \ eV$.According to the problem, we assume $U_2 = 0$. This implies we are adding a constant $C = 6.8 \ eV$ to the potential energy scale.The total energy $E_n$ of a hydrogen atom is given by $E_n = -13.6 / n^2 \ eV$.For $n = \infty$, the standard total energy is $E_{\infty} = 0 \ eV$.Since we shifted the potential energy scale by adding $6.8 \ eV$, the new total energy $E'_{\infty}$ will be $E_{\infty} + 6.8 \ eV = 0 + 6.8 \ eV = 6.8 \ eV$.

If the potential energy of a hydrogen atom in the first excited state is assumed to be zero, then the total energy of the $n = \infty$ state is,

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