It is possible to determine the ionization energy for hydrogen using the Bohr equation.Calculate the ionization energy (in kJ)for a mole of hydrogen atoms,making the assumption that ionization is the transition from n = 1 to n = ∞. A) 7.62 × 10³ kJ B) 2.76 × 10³ kJ C) 1.31 × 10³ kJ D) 3.62 × 10³ kJ E) 5.33 × 10³ kJ

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Quizplus · Accepted Answer

The ionization energy for hydrogen can be calculated using the Bohr equation for the energy levels of a hydrogen atom, which is given by $E_n = -\frac{2.18 \times 10^{-18}}{n^2}$ joules, where $n$ is the principal quantum number. For ionization, the electron goes from $n = 1$ to $n = \infty$, effectively reaching zero energy at $n = \infty$. The change in energy ($\Delta E$) is the ionization energy for one atom, and it is the difference between the energy at $n = \infty$ (which is 0) and the energy at $n = 1$. Thus, $\Delta E = 0 - (-2.18 \times 10^{-18} \, \text{J}) = 2.18 \times 10^{-18} \, \text{J}$ per atom. To find the ionization energy for a mole of hydrogen atoms, we multiply this value by Avogadro's number ($6.022 \times 10^{23} \, \text{mol}^{-1}$):$\Delta E_{\text{mole}} = 2.18 \times 10^{-18} \, \text{J/atom} \times 6.022 \times 10^{23} \, \text{atoms/mol}$$\Delta E_{\text{mole}} = 1.31 \times 10^{6} \, \text{J/mol} = 1.31 \times 10^{3} \, \text{kJ/mol}$Therefore, the correct answer is 1.31 × 10^3 kJ, which corresponds to choice C.

It Is Possible to Determine the Ionization Energy for Hydrogen