Download AP Physics Day 49

AP Physics Day 49 –Heisenberg Uncertainty Principle & Quantum Numbers
Date 2/5/2004
Overview:
HW Check & Review Ch 28: 1,3-6,9,15,36,38-40
challenge: 12
Notes – Lasers
Notes – deBroglie waves & Heisenberg Uncertainty Principle
HW:
Ch 28: 20,21,25,26,29,34,38-40
Papers:
None
Materials:
Demos:
ISPT program – different periodic tables
Websites:
For quantum numbers:
http://www.falstad.com/qmatom/
or copy in qmatom folder in quantum mechanics
the orbitron
http://www.shef.ac.uk/chemistry/orbitron/
useful links:
http://lpc1.clpccd.cc.ca.us/lpc/physics/modern.htm
Labs:
None
Notes:
Review Bohr & Debroglie
Now we have two views of electron in orbit – particle and wave (true for all subatomic particles)
But these look very different (particle is discrete and wave is spread out while waves move in a definite
way but particles can change a lot) how can we accommodate both these realities?
Notes – Heisenberg Uncertainty Principle
Simple explanation: when measuring position and momentum of a particle we need to “bounce”
something off of it to take a measurement. Usually we use a photon.
On everyday sized objects, the effect of one photon (or even billions of photons) is so small as to be
negligible, but if we are looking at a small object one photon can effect it quite a lot.
In our measurements we talk about the uncertainty in our value – this is the amount by which our
measurement is likely to be off. (Pace room – estimate 1 meter per pace ± 0.1 m)
Measuring small things is hard so we are very concerned about how precise our measurement is.
To pin down location we need to use something with a small wavelength (high frequency and high
energy) that means that it has more momentum to transfer to the particle when it hits which makes us
less certain about what its momentum is
To get momentum clearly we need to use low energy photon, but that doesn’t pin down location very
well…
x p ≤
h
2
There are deeper reasons for this equation, but they are not our concern here.
This destroys the simple idea of electrons orbiting around the nucleus in an atom.
have a well-defined position or momentum how can it go in a circle?
If the atom doesn’t
New wave mechanics are created – called quantum mechanics, with a new equation (the Schroedinger
equation) for finding the “wave function” of the particle.
Wave functions incorporate the wave nature of the particles, but now they have to fit around the nucleus
in three dimensions!
Wave functions keep the key characteristic of the Bohr model of the hydrogen atom – physical
quantities that you can measure for the electron are quantized! (Energy, angular momentum, etc)
Solution to wave function that describes “orbit” of electrons in referred to as an orbital because it is like
an orbit except that it is not well defined – it is more fuzzy
Notes – Quantum Numbers
When you solve the Schroedinger equation, you get out three quantum number (corresponding to the
three dimensions): n,l and ml. Can’t be solved exactly, but can get approximate solution that works
very well.
Bohr’s model had one quantum number n (only one dimension, r) and you could calculate anything you
wanted to know (energy, angular momentum) about orbit based on that n.
2mk2e4 1
h
En = - ( h2 )n2
mvr = n( )
2
and we could “see” the different energy levels by the photons emitted as the electron moved from one to
another.
In new model: Same basic idea but more complicated!
n is principal quantum number or shell quantum number & corresponds to the energy level in the Bohr
Model. It is still related to energy, but it does not tell you the energy of an electron by itself.
n = 1,2,3,…
From chemistry, remember that there is more than one electron in a shell. We will see how
many electrons each shell can hold
l is the orbital quantum number. Connected to the angular momentum of the orbit. Different angular
momentum for an orbital means different energy!
l = 0,…,(n-1)
h
) so Bohr’s solution was just one of the
2
allowed ones. Why didn’t he notice? Without other electrons around, all orbitals with same n
have same energy (called degenerate), so it doesn’t matter for hydrogen. It does matter for any
other element since they all have more electrons, which is why they had such a hard time
applying the Bohr model to other elements
Actually Bohr’s equation should have been: mvr = l(
From chemistry, different orbitals are given letters which are stand-ins for the l value!
l = 0 (s)
l = 1 (p)
l = 2 (d)
l = 3 (f)
l = 4 (g)
l = 5 (h)
ml is the magnetic quantum number. This has to do with the orientation of the orbit and the way that the
orbit’s angular momentum is oriented (Has to do with the way the electron “orbits” in the orbital.)
Outside of a magnetic field, it does not matter – all electrons in orbits with same angular
momentum (l) have same energy. But if there is a magnetic field it has effects on moving
electrons & will change the energy level of the orbit depending on how it is oriented compared to
magnetic field, now ml affects electron energy. Zeeman effect – you see that each line from an
atom splits into two or more lines in an electric field; actually used to measure the strength of the
magnetic field on the sun – measure how much lines of atoms on sun’s surface are split because
a stronger magnetic field splits lines more.
From chemistry, different orientation of “orbit” is why there are more than one of any orbital
Later studies turned up one more quantum number, ms, also called spin or spin quantum number.
Associated with the intrinsic angular momentum of the electron (which is why we call it spin
even though we don’t think the electron can be spinning.) Remember the orientation of the
angular momentum is important in a magnetic field (and there is a small magnetic field created
by a proton= in the nucleus). This shows up in fine measurements of hydrogen’s line spectrum
where each line is actually two very close lines. (True for spectra of many atoms, but in some
magnetic fields from even number of protons can cancel out!) There are two possible values of
ms, +1/2 or –1/2
So an electron in an atom has a particular set of quantum numbers that describe the orbital it is in and
the way that it orbits there.
Pauli Exclusion Principle – Under normal circumstances, there can only be one electron in an atom with
a given set of quantum numbers(n,l,ml,ms). This is why there are different numbers of electrons in
different shells or energy levels. – Periodic Table connection
Fix Quantum Numbers Notes
Introduce Quantum Numbers and show how orbitals differ based on quantum number
Then describe how energy varies for different quantum numbers