# Find the ionization energy of #"C"^(5+)#?

##### 2 Answers

#### Explanation:

Look for the *sixth ionization energy of carbon*.

Why the *sixth*? The ionization energy measures the energy required to *completely remove* one mole of electrons from one mole of the atoms at gaseous state.

The first ionization energy of an element, use one mole of *neutral* atoms as the reactant. Taking carbon as an example, the equation

characterizes this process.

Similarly

Note that each carbon nucleus contains

**Reference**

[1] Winter, Mark. “Carbon: Properties of Free Atoms.” Carbon»Properties of Free Atoms [WebElements Periodic Table], 27 Apr. 2018, www.webelements.com/carbon/atoms.html.

The ionization energy is

#### Explanation:

*hydrogen-like atom*. It has one electron and a nucleus with six protons.

Thus, you can use the **Rydberg formula** to calculate the energy.

Rydberg's original formula did not look directly at energies, but we can rewrite his formula to have these units.

The Rydberg formula for the change in energy is

#color(blue)(bar(ul(|color(white)(a/a) DeltaE = -R_HZ^2(1/n_text(f)^2 - 1/n_text(i)^2)color(white)(a/a)|)))" "#

where

To calculate the ionization energy from the ground state, we set

Thus, the energy required to ionize one atom is

On a molar basis, the ionization energy is