diagonal rule 1 the diagonal rule a simple use of 2 quantum numbers
TRANSCRIPT
diagonal rule
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The Diagonal RuleA simple use of 2 quantum
numbers
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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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Light is emitted from an atom when electrons in an atom move from an excited state configuration to the atom’s ground state configuration.
The lowest orbital (energy) arrangement for the electrons around the nucleus of an atom is know as the ground state of the atom.
Electron arrangements about the nucleus that are not the lowest possible energy arrangement are know as excited states.
The diagonal rule helps technicians, engineers and scientists determine the ground state arrangement of electrons about the nucleus of an atom.
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Light is emitted from an atom when electrons in an atom move from an excited state configuration to the atom’s ground state configuration.
The diagonal rule uses the first two quantum numbers
The diagonal rule helps technicians, engineers and scientists determine the ground state arrangement of electrons about the nucleus of an atom.
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123
the principal quantum numberthe angular momentum (azimuthal) quantum number
n
l
1,0
2,02,1
Two Quantum Number Bohr Atom Model
One Quantum Number Bohr Atom Model
“Random House Dictionary”
Note: There are only 5 words in my version of the Random House Dictionary that start with az. Can you name them?
(1) the arc of the horizon measured clockwise from the south point, in astronomy, or from the north point, in navigation. (2) the angle of horizontal deviation. Azimuthal adj.
Azimuth
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1,0
2,02,1
Each orbit is now described by two numbers. No orbit is described by the same two numbers. (There is no orbit called 0,0 or 1,1 or 2,2, etc)
1,0
2,02,1
3,0
Using the 2 quantum number, ,
(1)
(2) Is there an orbit labeled 3,3. nope!
(3) How many principal quantum number 4, orbits are there?
Three quick questions.
four 4,0 and 4,1 and 4,2 and 4,3
ln,
atom model, atom model, what would be the label for the next orbit after orbit 2,1?
Two Quantum Number Bohr Atom Model
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1,0
2,02,1
People are now in the habit of using letters instead of numbers for the azimuthal quantum number.
The letter “s” is used when the azimuthal quantum number value is 0.
The letter “p” is used when the azimuthal quantum number value is 1.
For example:
Each orbit is now described by two numbers.
The letter “d” is used when the azimuthal quantum number value is 2.
The letter “f” is used when the azimuthal quantum number value is 3.
Two Quantum Number Bohr Atom Model
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1s
2s2p
So we tend to describe the ground state for the nitrogen atom as
1,0
2,02,1
People also got tired of drawing the picture every time, thus a short hand notation was invented.
1s2 2s2 2p3
this exponent just tells us how many electrons are in the orbit.
Each orbit is now described by two numbers. Two Quantum Number Bohr Atom Model
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1,0
2,02,1Six more quick questions.
1s2 2s2 2p3this exponent just tells us how many electrons are in the orbit.
(1) What is the short hand notation for the ground state electron configuration of the carbon atom? (Remember that the carbon atom has 6 protons.) 1s2 2s2 2p2
(2) What about the helium atom? (The helium atom has 2 protons.)
1s2
Two Quantum Number Bohr Atom Model
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2p1s
3s2s
3p(3) How many:
3s orbits
3p orbits
3d orbits
n=1 orbits are there? n=2 orbits are there?
1s orbits2s orbits
2p orbits
n=4 orbits are there?
4s orbits
4p orbits
4d orbits
4f orbits
n=3 orbits are there?
1 234
Two Quantum Number Bohr Atom Model
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(4) How many:
3s 3p 3d
n=1 electrons are possible? n=2 electrons are possible?
1s
2s 2p
n=3 electrons are possible?
4s 4p 4d 4f
2 electrons
2 electrons 6 electrons( 8)
( 2)
2 electrons
n=4 electrons are possible?
6 electrons 10 electrons
(18)
2 electrons 6 electrons ?(32)
2p1s
3s2s
3p 3d
4d 4f4s 4p
Two Quantum Number Bohr Atom Model
1410 electrons
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2p1s
3s2s
3p 3d
4d 4f4s 4p
3s 3p 3d
1s
2s 2p
4s 4p 4d 4f
2
2 6
6
6
2
2
10
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The “ground” state for the atom with atomic number 60 is
(5)
true or false? (6)
The “ground” state for the carbon atom (atomic number 6) is
true or false? 1s2
2s1 2p3
False, the lowest energy state for the electrons of carbon is
1s2
2s2 2p2
True, the electrons are in the orbits that represent the lowest electron energy arrangement possible for the neodymium atom
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2p1s
3s2s
3p 3d
4d 4f4s 4p
Diagonal 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
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