Question

Energy Levels: An ionized atom having Z protons has had all but one of its electrons removed. If E is the total energy of the ground state electron in atomic hydrogen, then what is the total energy of the remaining electron in the ionized atom?

Answer 1

Step-by-step explanation:

Formula for energy value is as follows.

E =
`(-E_(0))/(n^(2))`

where,
`E_(0)` = 13.6

n = number of shell

So, at ground state energy of hydrogen atom will be as follows.

E =
`(-E_(0))/(n^(2))`

=
`(-13.6)/((1)^(2))`

= -13.6

Hence, for an ionized atom value of energy will be as follows.

E' =
`-13.6 * Z^(2)`

or, E' =
`E * Z^(2)`

Thus, we can conclude that total energy of the remaining electron in the ionized atom is
`E * Z^(2)`.