The ionization energy is the energy needed to remove an electron from an atom. In the Bohr model of the hydrogen atom, this means exciting the electron to the n = ∞ state. What is the ionization energy in kJ/mol, for hydrogen atoms initially in the n = 2 energy level?
A)290 kJ/mol
B)328 kJ/mol
C)656 kJ/mol
D)983 kJ/mol
E)1311 kJ/mol

Question

Quizplus · Accepted Answer

The ionization energy from the n = 2 level can be calculated using the Rydberg formula for the energy difference between levels in the hydrogen atom, which is given by $E = R_H \left( \frac{1}{n^2_{\text{initial}}} - \frac{1}{n^2_{\text{final}}} \right)$, where $R_H$ is the Rydberg constant (approximately $2.18 \times 10^{-18}$ J). For ionization, $n_{\text{final}} = \infty$ (which makes the second term zero) and $n_{\text{initial}} = 2$. Plugging these values in gives $E = 2.18 \times 10^{-18} J \times \left( \frac{1}{2^2} - 0 \right) = 5.45 \times 10^{-19} J$. To convert this energy to kJ/mol, we use Avogadro's number ($6.022 \times 10^{23} \text{mol}^{-1}$): $5.45 \times 10^{-19} J \times 6.022 \times 10^{23} \text{mol}^{-1} = 3.28 \times 10^5 J/mol = 328 kJ/mol$.

The Ionization Energy Is the Energy Needed to Remove an Electron