Question
Explain the excited states for the hydrogen atom.
✓
Answer
→At room temperature, most of the hydrogen atoms are in ground state.
→When a hydrogen atom receives energy by processes such as electron collisions, the atom may acquire sufficient energy to raise the
electron to higher energy states. The atom is then said to be in an excited state.
→Putting $n=2$ in
$\begin{array}{l}
E _{ n }=-\frac{13.6}{n^2} e V \\
E _2=-3.4 e V .
\end{array}$
→It means that the energy required to excite an electron in hydrogen atom to its first excited state, is an energy equal to
$\begin{aligned}
E _2- E _1 & =-3.40 eV -(-13.6) eV \\
& =-3.4 eV +13.6 eV \\
& =10.2 eV
\end{aligned}$
→Similarly, $E _3=-1.51 eV$
→To excite the hydrogen atom from its ground state to second excited state, energy required is
$\begin{aligned}
E _3- E _1 & =-1.51 eV -(-13.6) eV \\
& =-1.51 eV +13.6 eV \\
& =12.09 eV
\end{aligned}$
→In contrast, when an electron moves from an excited state to a lower energy state a photon is emitted.
→Thus, as the excitation of hydrogen atom increases (as $n$ increases) the value of minimum energy required to free the electron from the excited atom decreases.
→The energies of the excited states come closer and closer together as $n$ increases.
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