Fun with xrays Make your own at home! Sharp x-ray lines from atoms http://www.xray-art.com/ Science Friday with Nick Veasy http://www.nickveasey.com/

Quantum mechanics of matter What happens when we put an electron beam onto an aperture with two slits? What if the beam is weak enough that only one electron can get through at a time?

Quantum mechanics of matter Questions about atoms (1910) 1. Why do they radiate/absorb only in sharp lines? Classical planetary model Radiation expected: continuous spectrum. 2. Why don’t electrons radiate energy, fall into the nucleus, and atoms collapse?

Quantum mechanics of matter Niels Bohr (1913) H atomic lines can be explained if angular momentum is quantized…but no one knew why it was. Louis de Broglie (1924) If light, which we thought of as a wave, behaves as a particle, then perhaps matter particles behave as waves… and these “orbits” are like standing waves. deBroglie’s view of electron wave in atoms: only certain r, E allowed because l’s have to “fit” in a circle deBroglie’s view of electron wave in atoms: only certain r, E allowed because l’s have to “fit” in a circle

deBroglie waves of matter For photons he knew de Broglie wondered… is there also the same wavelength associated with matter? Confirmed by experiment! Electrons diffract from crystal surfaces like light in diffraction gratings! (each spot is a diffraction angle)

Erwin Schrodinger (1926) Modern wave equation found: atomic wavefunctions Y But what is “waving” in an atom? Y is a “probability amplitude”: The probability of finding an electron at a point in space is proportional to |Y|2 at each point!

Matter wavelengths note: 1 Å = 0.1nm=10-10 m. (size of H atom)

Electrons interfere through double slits, same as photons. P1. If we use faster electrons the diffraction pattern A. expands B. shrinks C. stays the same   P2. If we use a proton beam instead of electrons the diffraction pattern (same choices)

Interference of groups of sodium atoms, with speed 30m/s (cooled to 1 Kelvin)

Standing electron waves on a copper surface with iron atoms added, viewed by scanning tunneling microscope.

Heisenberg uncertainty principle Since matter is made of waves, we can’t know both the position and momentum of a particle with infinite precision

Heisenberg uncertainty principle Here’s why The only way to have zero uncertainty in the wavelength (Dp = 0) is to count infinite numbers of peaks. Then the particle’s position is spread out over all space (- to +).

Heisenberg uncertainty principle Here’s why A particle that is localized is actually a sum of waves with different l’s, so we that they cancel somewhere and add at other places!

Heisenberg uncertainty principle Adding these 8 waves gives the wave packet on the right. So if this a particle, the particle’s momentum uncertainty is at least:

Change from text The text uses The 4p is useful only in special cases, and where Dx, Dp are defined rigorously. It gives bad estimates (which is all we do here). We will use only:

These wavefunctions are “wavepackets” that represent particles moving in one direction P3. Which has the greatest average momentum (from the average wavelength)?

These wavefunctions “wavepackets” that represent particles moving in one direction, with about the same momentum P4. Which wavefunction has the greatest spread (uncertainty) in momentum? A. top B. bottom C. same

Can a particle be in “two places at once”? Can a wave?

Zero point energy of a confined particle If a particle is known to stay inside a “box” or atom or nucleus of size Dx, the particle’s average momentum is zero… it’s going right as often as left. But its uncertainty (spread) in momentum can’t be zero (because Dx is < ∞). So it must be moving most of the time with average speed vmin. Zero point energy!

Zero point energy of a confined particle Why called “zero-point” energy?. Because it is energy you have to build into the confined system from the start. You can’t get get the energy out, even at zero Kelvin, unless you break the system apart. For example, the atoms in a solid are always moving a little, even at zero kelvin.

We know why atoms don’t collapse! This death-spiral is impossible, because the electron can only lose (radiate) energy down to the “zero-point energy”, which we also call the “ground state” energy.

“Zero point energy” sounds too cool for the crazies (and movies) to leave alone. If you try “zero point” on YouTube, you get mostly nonsense about perpetual motion schemes (free energy).

P5. If we confine an electron and a proton to the same small space Dx (like inside a nucleus), which has the most “zero point” typical momentum? A. electron B. proton C. Same P6. If we confine an electron and a proton to the same space Dx, which has the most zero point kinetic energy? C. same Particles will less mass have more zero point energy for the same size of box.

Mr. Thompkins in (quantum) Wonderland

Mr. Thompkins in Wonderland

Bohr-Einstein “debates” (1920s) Einstein, stop telling God what to do God does not play dice!

Bohr-Einstein “debates” (1920s) Einstein, the photons you use would kick the electrons around! Why can’t I tell which slit an diffracting electron went through, with a microscope?