For hydrogen-like atoms, the ionization energy from the ground state is 13.6 eV. Which option correctly states this value?

For hydrogen-like atoms, the ionization energy from the ground state is 13.6 eV. Which option correctly states this value?

• A. 27.2 eV
• B. 13.6 eV
• C. 3.4 eV
• D. 6.8 eV

Answer: (B)

Ionization energy is the energy needed to take an electron from a bound state to zero energy at infinity. For hydrogen, the ground-state energy is -13.6 eV, so you must supply 13.6 eV to remove the electron completely. In hydrogen-like atoms with nuclear charge Z, the ground-state energy scales as -13.6 eV × Z^2, so the ionization energy becomes 13.6 eV × Z^2. With Z = 1 for hydrogen, the ionization energy from the ground state is 13.6 eV. The other values don’t match this full ionization energy.

Ionization energy is the energy needed to take an electron from a bound state to zero energy at infinity. For hydrogen, the ground-state energy is -13.6 eV, so you must supply 13.6 eV to remove the electron completely. In hydrogen-like atoms with nuclear charge Z, the ground-state energy scales as -13.6 eV × Z^2, so the ionization energy becomes 13.6 eV × Z^2. With Z = 1 for hydrogen, the ionization energy from the ground state is 13.6 eV. The other values don’t match this full ionization energy.