Consider the effective potential

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Presentation transcript:

Consider the effective potential What will be the effect of nonzero angular momentum on the electron? (A) electron will have large probability at the nucleus (B) electron has extremely low probability to approach nucleus

Consider the effective potential What will be the effect of nonzero angular momentum on the electron? (A) electron will have large probability at the nucleus (B) electron has extremely low probability to approach nucleus ħ2ℓ(ℓ+1) / 2mr2 -e2 / 4pe0r

How does the probability density look like at the nucleus? (A) There is a maximum at the nucleus for s-electrons, but it is zero for ℓ > 0 electrons with ℓ > 0 (p,d,f, etc.) (B) There is a maximum at the nucleus for all orbitals (C) The probability density is zero at the nucleus.

How does the probability density look like at the nucleus? (A) There is a maximum at the nucleus for s-electrons, but it is zero for ℓ > 0 electrons with ℓ > 0 (p,d,f, etc.) (B) There is a maximum at the nucleus for all orbitals (C) The probability density is zero at the nucleus. ... because of the factor r2 in the above expression (r = 0 at the nucleus).