Question

Ionization energy is the energy needed to eject an electron from an atom or ion. Calculate the ionization energy, IE, of the one-electron ion Be3 . The electron starts in the lowest energy level, n=1.

Answer 1

The energy of an electron in the n th Bohr orbit of a H-like atom ( one electron systems) like H,He⁺ ,Li⁺⁺ .Be⁺⁺⁺ etc is given by

E_n = - Z² x 13.6 eV / n²

Z = Atomic number ;     n = quantum number

For Be , Z = 4

Therefore for Be+++

E₁ = - 4² x 13.6 eV / 1² = - 217.6 eV

E₁ = - 217.6 eV means that when an electron at infinite distance falls into the first Bohr orbit, 217.6 eV energy is released (hence the negative sign).

Therefore the energy required to remove an electron in the first Bohr orbit to infinite distance is + 217.6 eV

Therefore,

the ionization energy of Be+++ = + 217.6 eV

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Ionization energy in Joules

1eV = 1.602 x 10 ^-19 J

Therfore, 217.6 eV = 217.6 x 1.602 x 10 ^-19 J = 3.48 x 10 ^-17 J

The ionization energy of Be⁺⁺⁺ = 3.48 x 10 ^-17 J

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