MHT CET · Physics · Atomic Physics
The ground state energy of hydrogen atom is \(-13.6 \mathrm{eV}\). When its electron is in the first excited state, its excitation energy is
- A \(3.4 \mathrm{eV}\)
- B \(6.8 \mathrm{eV}\)
- C \(10.2 \mathrm{eV}\)
- D zero
Answer & Solution
Correct Answer
(C) \(10.2 \mathrm{eV}\)
Step-by-step Solution
Detailed explanation
Given, ground state energy of hydrogen atom
\(
E_{1}=-13.6 \mathrm{eV}
\)
Energy of electron in first excited state
\(
\begin{array}{l}
\text { (ie, } n=2 \text { ) } \\
\qquad E_{2}=-\frac{13.6}{(2)^{2}} \mathrm{eV}
\end{array}
\)
Therefore, excitation energy
\(
\begin{aligned}
\Delta E &=E_{2}-E_{1} \\
&=-\frac{13.6}{4}-(-13.6) \\
&=-3.4+13.6=10.2 \mathrm{eV}
\end{aligned}
\)
\(
E_{1}=-13.6 \mathrm{eV}
\)
Energy of electron in first excited state
\(
\begin{array}{l}
\text { (ie, } n=2 \text { ) } \\
\qquad E_{2}=-\frac{13.6}{(2)^{2}} \mathrm{eV}
\end{array}
\)
Therefore, excitation energy
\(
\begin{aligned}
\Delta E &=E_{2}-E_{1} \\
&=-\frac{13.6}{4}-(-13.6) \\
&=-3.4+13.6=10.2 \mathrm{eV}
\end{aligned}
\)
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