lecture17a ch6 sec7 8

8/10/2019 Lecture17A Ch6 Sec7 8

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Tufts UniversityChem 1Fall 2013

Lecture 17AElectronic Structure of Many-Electron Atoms

Electronic

Structure

of Atoms

Nodes in Atomic Orbitals

The total number of nodes

in an orbital = (n - 1)

There are two kinds of

nodes:

angular nodes (aka

nodal planes); there are

l of them;

radial nodes; there are

(n 1 l) of them.

Problem. How many nodes and of which kind are

there in a generic 4d-orbital?

Electronic

Structure

of Atoms

Energies of Orbitals in H atom

The more nodes an orbitals

has, the more obstacles

there are for the electronic

motion, and the higher the

energy of the orbital.

For the hydrogen atom,

orbitals with the same

principal quantum numberhave the same energy.

Orbitals with the same

energy are called

degenerate.


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Electronic

Structure

of Atoms

Energy of Orbitals in the H Atom For the hydrogen atom, the

energy of an orbital depends

only on the principal

quantum number n.

For the H atom, there is a

simple formula to calculate

this orbital potential energy:

The 1s orbital has the lowest

energy and is known as the

ground state for the electron

in a hydrogen atom.Hydrogen atom

2

18

2

1018.2

n

J

n

hcRE H

Electronic

Structure

of Atoms

There are also multiple orbitals with higher

energy.

If the electron in an H atom occupies a higher

energy orbital, the atom (electron) is in an

excited state.

For the H atom, orbitals with the same n (same

shell) have the same energy.

Orbitals with the same energy are called

degenerate orbitals.

Electronic

Structure

of Atoms

Many-Electron Atoms For many-electron atoms, Schrodinger equation can not be

solved exactly (too difficult mathematically) and thewavefunctions are not available for them.

Only approximate calculations (estimations) are possible.

The estimated shapes oforbitals in many-electronatoms appear to be similarto those of the H atom.

Orbitals and their shapesobtained for the hydrogenatom are used for theother atoms (orbitalapproximation).

Electronic

Structure

of Atoms

Many-Electron Atoms

The most important difference

is that in many-electronatoms, the subshells havedifferent energy.

For example, the 2s and 2porbitals are degenerate in ahydrogen atom, but in all otheratoms the 2p orbitals havehigher energy than 2s.

There is no simple formula tocalculate the orbital energiesin many-electron atoms.

All atoms other than H

Electronic

Structure

of Atoms

Spin Quantum Number, ms

In 1925, it was discovered

that an electron has itsown quantum number, the

spin quantum number, ms

The spin quantum numberhas only 2 allowed values:

+1/2 and 1/2

Electronic

Structure

of Atoms

Pauli Exclusion Principle

No two electrons in the same atom can have

identical sets of quantum numbers (n, l, ml, ms).

One orbital can hold a

maximum of two electrons

and they must have

opposite spins.

Thus, an orbital in a

many-electron atom can

be empty, it can hold one

electron, or it can hold two

electrons

Lecture Problem. What is wrong with these sets of quantum numbers?

a) n = 0 l = 0 ml = 0 ms =1/2

b) n = 2 l = -1 ml = 0 ms = -1/2

c) n = 2 l = +1 ml = -2 ms =1/2

d) n = 3 l = 0 ml = 0 ms= 0


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Electron configurationsshow the distribution of electrons on an atom. They consist of

Number denoting the energy level

Letter denoting the type of orbital Superscript denoting the number of electrons in those orbitals

Lecture Problem.Give the orbital designations of one electron with these quantum numbers:a) n= 3 l= 0

b) n= 2 l= 1

c) n= 4 l= 2

d) n= 4 l= 3

Electronic

Structure

of Atoms

Orbital Diagrams

Each box (or shelf)

represents one orbital.

Half-arrows (or arrows)

represent the electrons.

The direction of the arrow

represents the spin of the

electron.

or

3

Electronic

Structure

of Atoms

Hunds Rule

For degenerate

orbitals, the lowest

energy is attained

when the number of

electrons with the

same spin is

maximized.

Oxygen atom

8 electrons

1s22s22p4

Electronic

Structure

of Atoms

Orbitals in many-

electron atoms are

filled in order of

increasing energy. This order can be

remembered from

either theAufbau

diagram (next slide)

or the Periodic Table

Building Up Principle

atoms other than H

Electronic

Structure

of Atoms

Aufbau = building up in German

We read this diagram column after column

Energy increases in order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, etc.

Aufbau Diagram

1 s

2 s p

3 s p d

4 s p d f

5 s p d f g

6 s p d f g h

7 s p d f g

8 s p d f

54p


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Building Up Principle of the Periodic Table

A better way to remember the order of increasing orbital energies is by using the Periodic Table

Four different blocks in the periodic table correspond to the type of orbital that has been filled last in anelement.

We write electronic configurations for an element starting from hydrogen and following all preceding

elements in order of increasing atomic number (H, He, Li, Be, etc.)

The number of the energy level (n) fors- andp-orbitals that are getting filled is the same as the period

number: e.g., in period 6, 6s- and 6p-orbitals are getting filled n is one less than the period number for d-orbitals, and two less for f-orbitals:

e.g, in period 6, 5d- and 4f-orbitals are getting filled

Lecture Problem

Write the electronic configurations ofa) Ne b) Na c) Fe d) Te e) W

Electronic

Structure

of Atoms

lecture17a ch6 sec7 8

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