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Multiple Choice
For a hydrogen atom, what is the energy (in electron volts, eV) of an electron in the n=4 excited state?
A
-1.51 eV
B
-0.85 eV
C
-3.40 eV
D
-13.6 eV
Verified step by step guidance
1
Recall that the energy levels of a hydrogen atom are given by the formula: $E_n = -13.6 \times \frac{1}{n^2}$ eV, where $n$ is the principal quantum number representing the energy level.
Identify the given energy level $n=4$ as the excited state for which we want to find the energy of the electron.
Substitute $n=4$ into the energy formula: $E_4 = -13.6 \times \frac{1}{4^2}$ eV.
Calculate the denominator $4^2 = 16$, so the expression becomes $E_4 = -13.6 \times \frac{1}{16}$ eV.
Multiply $-13.6$ by $\frac{1}{16}$ to find the energy of the electron in the $n=4$ state (do not compute the final value here, just set up the expression).