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Uncertainly Principle

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Electrons that receive enough extra energy from the outside world can leave the atom they are in.

Electrons that return to orbits they used to reside in give up the extra energy they acquired when they moved in the first place.

Electronic energy given up when electrons move back into an original orbit often shows up as a specific color light.

Electrons only change orbits if specific amounts (quanta) of extra energy from the outside world are involved.

Electrons that leave one orbit must move to another orbit.

Summary of Bohr’s Model (1913)

Electrons are in different orbits at fixed distances from nucleus.

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the last (little) twist!

Four Quantum Number Bohr Atom Model

2p1s

3s2s

3p 3d

4d 4f4s 4p

3, 2, -2, +1/22. the first 3d electron is labeled

3, 1,+1, -1/21. the last 3p electron is labeled

Finally

Na11

H1

Li3

K19

Bohr knew that:

The elements in the first column of the periodic table were:

Please remember that:

The last electron in each of these elements was a “s” electron.

1, 0, 0, +1/2

2, 0, 0, +1/2

3, 0, 0, +1/2

4, 0, 0, +1/2

Remember 0 is also the same a s.

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2p1s

3s2s

3p 3d

4d 4f4s 4p

3, 2, -2, +1/22. the first 3d electron is labeled

3, 1,+1, -1/21. the last 3p electron is labeled

Ar18

K19

Bohr knew that:

potassium's last electron was a “4s” electron.

3, 1, +1, -1/2

4, 0, 0, +1/2

argon’s last electron was a “3p” electron.

potassium has one more electron than argon.

The four quantum number model predicted that potassium’s last electron should be a 3d electron.

Four Quantum Number Bohr Atom ModelPlease remember

that:

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2p1s

3s2s

3p 3d

4d 4f4s 4pDiagonal Rule for Filling Bohr Model Orbits

3s 3p 3d

1s

2s 2p

4s 4p 4d 4f

2

6

6

6

2

2

10

10 14

2

5s2

Why is the 4s orbit filled before the 3d orbit?

Four Quantum Number Bohr Atom Model

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Electrons within an atom can be completely identified as unique electrons with the aid of 4 quantum numbers.

the principal quantum number

the angular momentum (azimuthal) quantum number

n

l

the magnetic quantum number

m

the electron spin quantum number

s

These 4 quantum numbers are called:

No two electrons in the same atom can have the same value for all four of these quantum numbers.

Why is the 4s orbit filled before the 3d orbit?

2p1s

3s2s

3p 3d

4d 4f4s 4p

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Atoms are filled with electrons from the orbit closest to the nucleus to the orbit furthest from the nucleus.

Electrons returning to their “ground” state can emit light with a unique frequency (energy).

The diagonal fill rule predicts the way electrons fill orbits.

The Bohr model does not explain why the 4s orbit is filled before the 3d orbit.

Why is the 4s orbit filled before the 3d orbit?

A revised model is needed to provide this explanation.

2p1s

3s2s

3p 3d

4d 4f4s 4p

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Heisenberg’s Uncertainty Principle(1927)

Schrodinger’s ideas (1926)

Planck’s ideas (1900)

Einstein's ideas (1905)

DeBroglie’s ideas (1924)

But he wondered why the Schrodinger wave equation did not work very well when there was more than one electron in the atom.

Heisenberg understood and agreed with:

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Heisenberg’s Uncertainty Principle(1927)

Heisenberg believed that:

mv

• Both the position, x, and momentum, p, of a moving electron in a wave circular path around the nucleus of an atom is not exactly known at the same time.

• DeBroglie’s equation worked but the problem was we did not really know the exact value for momentum,p, to use.

• the exact value for lambda in the DeBroglie equation could not be determined since the exact value for the electron momentum, mv, was not know.

hhp

lambda =

(Momentum, p, is always equal to the mass of a moving object times its velocity)

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Heisenberg’s Uncertainty Principle(1927)

Heisenberg was able to conclude that:

• Schrodinger’s wave equation would not describe electron movement around the nucleus very well since the electron’s wavelength would never be known with exact certainty.

• Although Heisenberg could not work out what the exact uncertainty in the momentum value of a moving electron was, he was able to determine what the smallest value of the product of the distance uncertainty, , and the momentum uncertainty would be .

x[ ]mv[ ]

uncertainty in momentum value

( ) uncertainty in position value

( ) is equal to or greater than 4

h

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4

h

Heisenberg’s Uncertainty Principle(1927)

Heisenberg was able to conclude that:

(mv)[ ]

x[ ] p[ ]

4

hx[ ]

uncertainty in momentum value

uncertainty in position value

is equal to or greater than 4

h

error in momentum value

error in position value

( )( )

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The Post Bohr Atom

By 1930, a new picture of the electron arrangement and position had developed and this theory is the one still used today.

• An electron’s position is not possible to determine.

• It is only possible to determine the probability of where an electron might be at any given instant of time.

• The solution to the Wave Equation for a range of uncertain x values determines the 3-D shapes about the atom’s nucleus within which electrons will most likely be located.

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That is to say, the probability (odds) of finding the electron in that region are very high. (but not 100%)

The electrons in Bohr’s first orbit DO NOT circle the nucleus.

There is just a spherical region near the nucleus where that electron is most likely to be found.

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There is just a spherical region near the nucleus where that electron is most likely to be found.

The electrons in Bohr’s second orbit DO NOT circle the nucleus.

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There are three different, two-part, but isolated regions perpendicular to each other where these electrons are likely to be found.

here

or here

hereor here hereor here

The electrons in Bohr’s third orbit DO NOT circle the nucleus.

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An electron can also be located further from the nucleus in one of 5 d regions.

There are five different multiple but isolated regions perpendicular to each other where that electron is likely to be found.

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The Post Bohr Atom

This new picture of the electron arrangement and position about the nucleus answers many of Bohr’s questions.

One of the first questions that was answered was why the DIAGONAL RULE for filling orbitals with electrons works.

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• Electrons did not orbit the nucleus like a moon around a planet.

By the 1930’s it was understood that:

2p1s

3s2s

3p 3d4s

• The exact position of an electron about the nucleus could not be determined.

• The probability (odds) of finding an electron in a specific region about the nucleus could be determined.

• “s” electron regions (locations where an “s” electron is most likely to be) are shaped like spheres.

“1s” electron region

“2s” electron region

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• electrons did not orbit the nucleus like a moon around a plant.

2p1s

3s2s

3p 3d4s

• “s” electron regions (locations where an “s” electron is most likely to be) are shaped like spheres.

“1s” electron region

“2s” electron region

A “2s” electron is likely to be found in a spherical region that is larger from the nucleus than the “1s” electron.

A“3s” electron region is an even larger spherical region than the “2s” region.

A“4s” electron region (sphere) is larger than the “3s” region.

By the 1930’s it was understood that:

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2p1s

3s2s

3p 3d4s

Remember these shapes just represent the most likely place to find a “p” electron.

• There are 3 “p” electron regions, px, py, and pz.

“p ”

x

“p ”

y

“p ”

z

• A “p” electron region (locations where an “p” electron is most likely to be) is shaped like 2 spheres, one on each side of a nucleus.

Low chance of finding a p electron here.

y

High chance of finding a p electron here.

y

High odds of finding a p electron here.

y

High chance of finding a p electron here.

z

By the 1930’s it was understood that:

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2p1s

3s2s

3p 3d4s

Remember these shapes just represent the most likely place to find a “d” electron.

“p ”

z

• A “d” electron region (locations where a “d” electron is most likely to be) has 5 unique shapes.

By the 1930’s it was understood that:

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2p1s

3s2s

3p 3d4s

• The 4s region has a very large radius out from the nucleus and represents a very large spherical space.

• There is a high probability that an electron will go into the 4s region instead of the 3d region because the 4s region overlaps some of the 3d region space.

Thus, the diagonal rule works, that is to say, the 4s region will fill up before an electron enters the 3d region.

What orbit starts to fill after the 3d orbit has been filled?

4p

By the 1930’s it was understood that:

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