pp - Variation of Ionization Energy with Atomic Number For...

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Variation of Ionization Energy with Atomic Number For a many electron atom E PE = -<Ze 2 /r > Here the brackets represent an average -- we must take an average because the electron does not remain at one fixed value of r . Earlier, we noted that E orb = -Ze 2 /2 <1/r> These averages are dominated by contributions at SMALL r. When r is SMALL , (1/r) is LARGE ; thus, the larger the fraction of its time an electron spends at SMALL r, the MORE NEGATIVE -Ze 2 /2 <1/r> will be,and the ELECTRON will be "BOUND" MORE TIGHTLY to the nucleus (i.e E orb will be more NEGATIVE) Four factors determine the value of E orb 1. Increasing Nuclear Charge Ze 2. Screening Effects 3. Electron Repulsion Effects 4. Value of <1/r> The predominant screening of VALENCE ELECTRONS is by INNER SHELL (OR CORE) ELECTRONS i.e. Valence electrons are predominantly screened by ELECTRONS OF LOWER PRINCIPAL QUANTUM NUMBER s, p, d, f . ... electrons of a given principal quantum number PENETRATE to the nucleus to different extents ns > np > nd > nf -- thus ns electrons are screened (by inner electrons) LESS than np electrons which are screened LESS than nd electrons etc. • Electrons of the SAME PRINCIPAL QUANTUM NUMBER screen each other -- this is a SMALLER EFFECT and we will treat it as a secondary effect in our discussions Observation Rationale I 1 (He) > I 1 (H) Increasing Z modified by electron repulsion I 1 (Li) < I 1 (He) Z increases from 2 to 3, but SCREENING of 2s electrons by 1s electrons largely offsets this with the result that Z eff is much closer to 1 . In addition, since the 2s electron spends MOST of its time
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FURTHER from the nucleus than does the 1s electron, <1/r> 2s < <1/r> 2s Both factors serve to make I 1 (Li) SMALL I 1 (Be) > I 1 (Li) Z increases from 3 to 4; imperfect screening of 2s electrons by the 1s electrons results in 2 < Z eff < 4.
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pp - Variation of Ionization Energy with Atomic Number For...

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