Question

Question #2fc5b

Answer 1

You can do it like this:

Explanation:

The effective nuclear charge `sf(Z_"eff")`, experienced by an electron is less than the nuclear charge `sf(Z)` because of the shielding effect of the other electrons:

`sf(Z_(eff)=Z-s)`

Where `sf(s)` is the shielding constant.

We can calculate `sf(s)` by applying Slater's Rules:

Electrons are grouped together in increasing order of `sf(n)` and `sf(l)` values. `sf(n)` tells you the number of the energy level and `sf(l)` denotes the sub - shell such as `sf(s, p, d)`. Because `sf(s)` and `sf(p)` electrons are close in energy they are grouped together:

`sf([1s][2s,2p][3s,3p][3d][4s,4p][4d][4f][5s,5p])` and so on.

You can calculate the screening constant as follows:

Add 0.35 for each other electron within the same group, except for `sf[1s]` when this is 0.3

If the group is of the `sf(["ns,np"])` type you add an amount of 0.85 for each electron with a principal quantum number of `sf((n-1))` and an amount of 1.00 for each electron with a quantum number of `sf((n-2))` or less.

For `sf([d])` and `sf([f])` electrons just add 1.00 for each electron which is closer to the nucleus.

Lets apply this to `sf(""_25Mn)`:

The electron structure is:

`sf([1s^(2)][2s^(2)2p^(6)][3s^(2)3p^(6)][3d^(5)][4s^(2)])`

For a 3d electron:

Within the 3d group there are 4 other electrons giving 4 x 0.35 = 1.40 units.

There are 18 other electrons closer to the nucleus giving 18 x 1.00 =18.0 units.

`:.` `sf(s=1.40+18.0=19.4)` units.

`:.` `sf(Z_(eff)=25-19.4=5.6)` units.

For a 4s electron:

Within the 4s group there is 1 other electron giving 1 x 0.35 = 0.35 units.

In the (n - 1) group, which are the 3s, 3p and 3d, electrons there are 13 electrons giving 13 x 0.85 = 11.05 units

This leaves 10 (n - 2) electrons. This gives 10 x 1 = 10 units.

`:.` `sf(s=0.35+11.05+10=21.4)` units.

`:.` `sf(Z_(eff)=25-21.4=3.6)` units.

This shows that the 4s electrons experience a smaller effective nuclear charge than the 3d electrons so are more easily lost

This is consistent with observations.