Knowing the Energy of a photon, what is the charge of a species?

[brbrett]

Homework Statement

An atom or ion with only one electron is excited from the ground state to the first excited state (n = 2) with a photon of 1.47E-17 J of energy. What is the charge on the one-electron species?
A. 0
B. +1
C. +2
D. +3
E. +4

Homework Equations

E=-(2.18E-18)(Z²)/(N²)

The Attempt at a Solution

I plugged in the information given into the equation:

(1.47E-17)=(-2.18E-18)(Z²)((1/4)-1)

With some algebra, I got Z=2.998, which may as well be a charge of +3.
However, according to the answer key, the correct answer is, in fact, +2 (C).
I would appreciate any guidance as to where I might be going wrong with this problem. :)

 

[Orodruin]

What is the charge of the ion as a whole if the charge of the nucleus is 3?

 

[brbrett]

Due to shielding, the effective charge would be about +2? I think I kinda see that maybe my calculations weren't wrong, but that I didn't understand the question right, but I still don't really get it.

 

[Borek]

You calculated Z, but Z is not what the question asks about. It asks you to calculate charge of the ion, not of the nucleus.

 

[brbrett]

Ah, so then because I calculated the nucleus' charge to be +3, with a single electron there would be a charge of +2? That would make a lot of sense. Then I assume I didn't make any mistakes in solving for charge of the nucleus to figure out the ion's charge? Thanks!

 

[Borek]

Looks OK, although your first equation and the second equation are different.

 

[brbrett]

Thanks!