Calculate the ground-state energy of C5+ ion?

Question

Hi

I am in need of some help with the following!

How do you calculate the ground state energy of a C5+ ion (i.e. for n=1) and the energy of the next three highest energy levels (i.e. for n=2, 3,4). Express your answers in ev.

Thanks

Answer 1

C⁵⁺-ion is an atom with a single electron. So the predictions of the Bohr-model hold for this ion. According to Bohr model the energy of an electron orbiting at level n around a nucleus with Z protons is given by:

E(n) = - RE · Z² / n²

RE is a constant: the Rydberg energy. It is defined as:

RE = k²·e⁴·me/ (2·ħ²) = 13.6eV

with

k Coulomb's constant, e elementary charge, me mass of electron at rest, ħ Dirac constant = reduced Planck constant

For derivation of the formulas follow link below.

So for the C⁵⁺-ion with Z=6

E(n) = -13.6eV · 6² / n² = -489.6eV/n²

=>

E(1) = - 489.6eV

E(2) = -122.4eV

E(3) = - 54.4eV

E(4) = - 30.6eV

...