Question

The ionization (binding) energy of the outermost electron in boron is 8.26 eV. (a) Use the Bohr model to estimate the “effective charge,” Zeff , seen by this electron. (b) Estimate the average orbital radius.

Answer 1

The effective nuclear charge may be defined as the actual nuclear charge (Z) minus the screening effect caused by the electrons intervening between the nucleus and valence electron.

The effective nuclear charge ($Z_{\mathrm{eff}}$) is the net positive charge experienced by an electron in a multi-electron atom.

eff

where

Z is the number of protons in the nucleus (atomic number), and

S is the average number of electrons between the nucleus and the electron or Called as Screening or Shielding Constant.

S= 1*N2+0.85*N1+0.35*N0 where No of othere electron in the same shell N0, No of othere electron in the next smaller shell N1 an so on

= 0.35*2+0.85*2=2.40

Zeff = 5-2.4=2.6.

Calculation of Radius

For Boron atomic no is 5. Essential centripetal force for the elctron in the outer shell is provided by the elctrostatic attactive force between nucleus and that electron

M V² / r =1/4π E₀ ( 5e²/ r²⁾

Subtstitute the values and we get r = 8.13*10 ^-11 (detailed calculation is shown in the fig attached
2 2 2. 112 get.炎 2
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