Calculate the screening constant of alkali metals for valenvy electrons.

Answer

`Li = 1.7, Na = 8.8; K = 16.8, Rb = 34.8, Cs = 52.8`

Explanation

a. Electronic configuration of `Li (Z=3)` is
`(1s^(2))/((n-1)), (2s^(1))/(n)`
`(sigma)_(2s^(1)) = [0.85 xx "No. of electrons in (n-1)th shell"]`
`= 0.85 xx 2 = 1.7`
b. `Na(Z = 11) = 1s^(2), (2s^(2) 2p^(6))/((n-1)), (3s^(1))/(n)`
`(sigma)_(3s^(1)) = [[(0.85 xx "No. of electrons in (n-1)th shell")],[+1.00 xx "Total no. of electrons"],["in the inner shell"]]`
`= (0.85 xx 8) + (100 xx 2) = 8.8`
c. `K(Z=19) = (1s^(2),2s^(2) 2p^(6))/("inner" e^(-)'s),(3s^(2) 3p^(6))/((n-1)), (4s^(1))/(n)`
`(sigma)_(4s^(1)) = [[(0.85 xx "No. of electrons in (n-1)th shell")],[+1.00 xx "Total no. of electrons"],["in the inner shell"]]`
`= (0.85 xx 8) + (1.00 xx 10) = 16.8`
d. `Rb(Z=37) = (1s^(2),2s^(2)2p^(2), 3s^(2) 3p^(6) 3d^(10))/("inner" e^(-)'s), (4s^(2) 4p^(6))/((n-1)),(5s^(1))/(n)`
`(sigma)_(5s^(1)) = [[(0.85 xx "No. of electrons in (n-1)th shell")],[+"("1.00 xx "Total no. of electrons"],["in the inner shell"")"]]`
e. `Cs(Z=55) = (1s^(2),2s^(2)2p^(6), 3s^(2) 3p^(6) 3d^(10))/("inner" e^(-)'s)`,
`(5s^(2) 5p^(6))/((n-1)),(6s^(1))/(n)`
`(sigma)_(5s^(1)) = [[(0.85 xx "No. of electrons in (n-1)th shell")],[+"("1.00 xx "Total no. of electrons"],["in the inner shell"")"]]`
`= (0.85 xx 8) + (1.00 xx 46) = 52.8`