Question

How much energy is required to ionize an He^+ ion in its ground state?

The answer is 8.72 X 10^-18 J but I don't know how to find that.

Answer 1

`E = 8.720 × 10^"-18" color(white)(l)"J"`

Explanation:

The energy `E` required to ionize a hydrogen-like ion is given by the Rydberg energy equation

`color(blue)(bar(ul(|color(white)(a/a)E = R_text(E)Z^2color(white)(a/a)|)))" "`

where

`R_text(E) =` the Rydberg constant in energy units (joules)
`Zcolor(white)(ll) =` the atomic number of the atom

For a helium ion, `Z = 2`

Also, `R_text(E) = 2.180 × 10^"-18"color(white)(l) "J"`

∴ `E = 2.180 × 10^"-18"color(white)(l) "J" × 2^2 = 4 × 2.180 × 10^"-18"color(white)(l) "J" = 8.720 × 10^"-18"color(white)(l) "J"`