Which of the following atoms/ions have a ground state energy of -54.4 eV?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Singly-ionised helium
Bohr's model applies to any one-electron atom or ion of atomic number \( Z \). Its energy in level \( n \) is
\( \displaystyle E_n = -\frac{13.6\,Z^{2}}{n^{2}}\,\mathrm{eV} \)
In the ground state \( n = 1 \), so
\( \displaystyle -13.6\,Z^{2} = -54.4 \;\Rightarrow\; Z^{2} = 4 \;\Rightarrow\; Z = 2 \)
A one-electron system with \( Z = 2 \) is helium that has lost one electron, \( \mathrm{He^{+}} \).