Question

The energy of the electron in third excited state of the hydrogen atom is

• A. -0.54 eV
• B. -1.51 eV
• C. -13.6 eV
• D. -3.4 eV
• E. -0.85 eV

Hint:

Excited state $x \Rightarrow n = x + 1$.

Answer 1

Answer: (E)

Step 1: Concept
Energy in $n^{th}$ state is $E_n = \frac{-13.6}{n^2} \text{ eV}$.

Step 2: Meaning
"Third excited state" means the electron is in the $n = 4$ energy level.

Step 3: Analysis
$E_4 = \frac{-13.6}{4^2} = \frac{-13.6}{16} = -0.85 \text{ eV}$.

Step 4: Conclusion
Hence, the energy is -0.85 eV.
Final Answer: (E)