Uncertainty Principle 1 Uncertainly Principle

Uncertainty Principle 2 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.

Uncertainty Principle 3 the last (little) twist! Four Quantum Number Bohr Atom Model 2p2p 1s1s 3s3s 2s2s 3p3p 3d3d 4d4d4f4f4s4s4p4p 3, 2, -2, +1/22. the first 3d electron is labeled 3, 1,+1, -1/21. the last 3p electron is labeled Finally Na 11 H 1 Li 3 K 19 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.

Uncertainty Principle 4 2p2p 1s1s 3s3s 2s2s 3p3p 3d3d 4d4d4f4f4s4s4p4p 3, 2, -2, +1/22. the first 3d electron is labeled 3, 1,+1, -1/21. the last 3p electron is labeled Ar 18 K 19 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 Model Please remember that:

Uncertainty Principle 5 2p2p 1s1s 3s3s 2s2s 3p3p 3d3d 4d4d4f4f4s4s4p4p Diagonal Rule for Filling Bohr Model Orbits 3s3s3p3p3d3d 1s1s 2s2s2p2p 4s4s4p4p4d4d4f4f s5s 2 Why is the 4s orbit filled before the 3d orbit? Four Quantum Number Bohr Atom Model

Uncertainty Principle 6 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 numberm 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? 2p2p 1s1s 3s3s 2s2s 3p3p 3d3d 4d4d4f4f4s4s4p4p

Uncertainty Principle 7 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. 2p2p 1s1s 3s3s 2s2s 3p3p 3d3d 4d4d4f4f4s4s4p4p

Uncertainty Principle 8 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:

Uncertainty Principle 9 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. h h p  lambda =  (Momentum, p, is always equal to the mass of a moving object times its velocity)

Uncertainty Principle 10 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 

Uncertainty Principle 11 4 h  Heisenberg’s Uncertainty Principle(1927) Heisenberg was able to conclude that: (mv)  [] x  [] p  [] 4 h  x  [] uncertainty in momentum value uncertainty in position value is equal to or greater than 4 h  error in momentum value error in position value ()()

Uncertainty Principle 12 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.

Uncertainty Principle 13 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.

Uncertainty Principle 14 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.

Uncertainty Principle 15 There are three different, two-part, but isolated regions perpendicular to each other where these electrons are likely to be found. here or here here or herehere or here The electrons in Bohr’s third orbit DO NOT circle the nucleus.

Uncertainty Principle 16 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.

Uncertainty Principle 17 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.

Uncertainty Principle 18 Electrons did not orbit the nucleus like a moon around a planet. By the 1930’s it was understood that: 2p2p 1s1s 3s3s 2s2s 3p3p3d3d 4s4s 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

Uncertainty Principle 19 electrons did not orbit the nucleus like a moon around a plant. 2p2p 1s1s 3s3s 2s2s 3p3p3d3d 4s4s “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:

Uncertainty Principle 20 2p2p 1s1s 3s3s 2s2s 3p3p3d3d 4s4s Remember these shapes just represent the most likely place to find a “p” electron. There are 3 “p” electron regions, p x, p y, and p z. “p ” x y 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:

Uncertainty Principle 21 2p2p 1s1s 3s3s 2s2s 3p3p3d3d 4s4s 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:

Uncertainty Principle 22 2p2p 1s1s 3s3s 2s2s 3p3p3d3d 4s4s 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? 4p4p By the 1930’s it was understood that:

Uncertainty Principle 23