Ground state of Potassium and Hydrogen

[shyguy79]

Homework Statement

For potassium in ground state configuration (Z=19) how would you expect the energy of the least tightly bound electron to compare with the energy of the electron in hydrogen excited to a state of the same principal quantum number n. Explain your answer.

Homework Equations

None

The Attempt at a Solution

Ok, so in it's ground state in standard notation Potassium 19 is:

K 1s$^{2}$ 2s$^{2}$ 2p$^{6}$ 3s$^{2}$ 3p$^{6}$ 4s$^{1}$

I'm guessing that the principal quantum number that it's asking for is when n=4 in the hydrogen? If so where do I go from here?

Any help is gratefully received

 

[shyguy79]

Is it perhaps that when the quantum number n=4 in the hydrogen atom the eV value ≈ -0.85eV (-13.6ev/4^2)? Because the angular momentum quantum number l = 0 then it has less energy and is closer to the nucleus?

I'm kinda clutching at straws

 

[einstein1921]

1s 2 2s 2 2p 6 3s 2 3p 6 electron will screen the nucleus of K, it seems that the 4s electron is attracted by 1 charge(19-18),but it doesn't screen so good,so the 4s electron will see more than 1 charge,for example 2,this situation will increase the attraction force to the 4s electron resulting in the decreasing of the energy.In contrast to hydrogen atom ,the nucleus is just 1 charge.so the energy of 4s electron will lower than that of the 4s electron of hydrogen.

 

[Rooted]

Hmmm, interesting question. I have a feeling the energy equation for hydrogenic atoms are related to the eigenvalue n like this;

E= -(e²/8πε₀a₀) Z²/n²I'll try and find a reference... hang on a sec

Edit - does this page help at all? http://electron6.phys.utk.edu/phys250/modules/module 3/Multi-electron atoms.htm

 

[Nickie]

The ground state configuration of potassium has one electron in its outermost shell, in the 4s orbital. This electron is less tightly bound compared to the electron in hydrogen in the same principal quantum number n=4. This is because potassium has a higher nuclear charge (Z=19) compared to hydrogen (Z=1), which results in a stronger attraction between the nucleus and the outer electron. This stronger attraction leads to a lower energy for the outer electron in potassium compared to the outer electron in hydrogen.

In addition, the outer electron in potassium also experiences shielding from the inner electrons, which reduces its effective nuclear charge and further lowers its energy. On the other hand, the outer electron in hydrogen does not experience any shielding and thus has a higher energy compared to the outer electron in potassium.

Overall, the outer electron in potassium is expected to have a lower energy compared to the outer electron in hydrogen in the same principal quantum number n=4.