Solving Nature of Atoms Homework: Part (a) ionization energy Z=2

[arod2812]

Homework Statement

(a) What is the minimum energy (in electron volts) that is required to remove the electron from the ground state of an ionized atom (Z=2)? (b) What is the ionization energy for this ion?

Homework Equations

After doing what I got the answer for part (b)... but I don't know what part (a) requires. I thought this number would be 13.6 eV, but it's not. What exactly is part (a) asking?

The Attempt at a Solution

I used the equation E= -13.6*(Z^2/n^2). I plugged in 2 for Z and 1 for n.

 

[Astronuc]

13.6 eV is the ionization of atomic hydrogen. In ionziation, the electron is completely removed as opposed to simply moved up to an excited state in the atom.

Z=2 is of course He.

See - http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html - for hydrogen

http://hyperphysics.phy-astr.gsu.edu/hbase/atomic/grotrian.html
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/helium.html

 

[Moetasim]

This gave me an answer of -54.4 eV. However, this negative value does not make sense for ionization energy.

Part (a) is asking for the minimum energy required to remove an electron from the ground state of an ionized atom with Z=2. This means that the atom already has a positive charge of +2, and the electron is being removed from this positively charged ion.

The equation you used, E= -13.6*(Z^2/n^2), is the Rydberg formula for calculating the energy levels of a hydrogen atom. However, it is not applicable for this problem since we are dealing with an ionized atom with Z=2, not a hydrogen atom.

To calculate the ionization energy, we need to use the equation E= -R*(Z^2/n^2), where R is the Rydberg constant (13.6 eV) and n is the principal quantum number of the electron being removed. Since we are dealing with an ionized atom, the principal quantum number of the electron in the ground state is n=1. Therefore, the ionization energy for this ion with Z=2 is E= -13.6*(2^2/1^2)= -13.6*4= -54.4 eV.

It is important to note that the negative sign in front of the ionization energy indicates that energy is required to remove the electron from the ion. This is because the electron is being removed from a positively charged ion, so energy must be added to overcome the attractive force between the positively charged ion and the negatively charged electron.

In conclusion, the minimum energy required to remove an electron from the ground state of an ionized atom with Z=2 is 54.4 eV, and the ionization energy for this ion is also 54.4 eV.