Question #2fc5b

1 Answer
Feb 10, 2017

Answer:

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.