Today: Examples of Tunneling

Transcription

1 Today: Examples of Tunneling 1. Last time: Scanning tunneling microscope. 2. Next: Alpha particle tunneling HWK13 Postponed until next week.

2 STM (picture with reversed voltage, works exactly the same) end of tip always atomically sharp

3 How sensitive to distance? Need to look at numbers. T ~e -2 a how big is? (= 1/(how long is exponential tail of wave function = how far can tunnel). α = 2m(V 0 E) Calculate: if V 0 -E = 4 ev, = 1/(1 x m) So if a is 3 x m, T = e -6 =.0025 add 1 extra atom (d ~ m), how much does T change? T = e -4 =.018 so one atom more 7x the current!

4 actual STM moves tip across surface, adjusts distance to keep distance constant, keeps track of how much has to move in and out to make map.

5 Radioactive alpha decay Nucleus is unstable emits a particle Typically found for large atoms with lots of protons and neutrons. Alpha Decay: Nucleus emits an alpha particle An alpha particle is 2 neutrons and 2 protons. Radon protons, 136 neutrons Proton (positive charge) Neutron (no charge) Nucleus has lots of protons and lots of neutrons. Two forces acting in nucleus: - Coulomb force.. Protons really close together, so very big repulsion from coulomb force - Nuclear force (attraction between nuclear particles is very strong if very close together) called the STRONG Force.

6 Radioactive decay Proton (positive charge) Neutron (no charge) Radon protons, 136 neutrons In alpha-decay, an alpha-particle is emitted from the nucleus. This raises the ratio of neutrons to protons makes for a more stable atom. (Neutron are neutral.. no coulomb repulsion, but nuclear force attraction)

7 How does this happen Starting point always to look at potential energy curve for particle Nucleus (Z protons, Bunch o neutrons) New nucleus (Z-2 protons, + Alpha particle (2 protons, Bunch o neutrons) 2 neutrons) Look at this system as the distance between the alpha particle and the nucleus changes. As bring closer, What happens to potential energy? (Z-2) V=0 At a great distance

8 How does this happen Starting point always to look at potential energy curve for particle As bring closer, what happens to potential energy? V=0 At a great distance A V(r) r C V(r) r B V(r) D. Something else r

9 How does this happen Starting point always to look at potential energy curve for particle As bring closer, What happens to potential energy? V=0 At a great distance B V(r) kqq 1 2 k( Z V ( r) r 2)( e)(2e) r Takes energy to push towards the nucleus, so potential energy must increase.

10 How does this happen Starting point always to look at potential energy curve for particle V(r) 30 MeV 4 to 9MeV of KE Edge of the nucleus (~8x10-15 m), Nuclear (Strong) force starts acting Strong attraction between nucleons Potential energy drops dramatically

11 Starting point always to look at potential energy curve for particle Energy Bring alpha-particle closer Coulomb &Nuclear 30 MeV V(r) Coulomb force dominates kqq 1 2 k( Z V ( r) r 2)( e)(2e) r r Edge of the nucleus (~8x10-15 m), Nuclear (Strong) force starts acting Strong attraction between nucleons Potential energy drops dramatically

12 Nuclear Physics Sim

13 Observations show Alpha-particles exit with a range of energies V(r) 30 MeV 4 to 9MeV of KE Inside particle can form and has lots of KE

14 How does this happen Starting point always to look at potential energy curve for particle V(r) 30 MeV 4MeV of KE 100MeV of KE

15 Observe -particles from different isotopes (same protons, different neutrons), exit with different amounts of energy. 30 MeV (Same peak height if protons same) V(r) 2 Decay constant: ( V E) 2 m 9MeV KE 4MeV KE Was one or the other more likely to tunnel through? And WHY??? a. the 9MeV alpha particle was more likely b. the 4MeV alpha particle was more likely c. both had the same probability of tunneling

16 Observe a particles from different isotopes (same protons, different neutrons), exit with different amounts of energy. 2 ( V E) 2 m V(r) 30 MeV 1. Less distance to tunnel, 2. Decay constant always smaller 3. Wave function doesn t decay as much before reaches other side more probable! 9MeV KE 4MeV KE Answer is a. The 9 MeV electron more probable Isotopes that emit higher energy alpha particles, have shorter lifetimes!!!

17 Solving Schrodinger equation for this potential energy is hard! V(x) Square barrier is much easier and get almost the same answer! V(x)

18 Quantum Tunneling Sim

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20 Rest of today: other applications of tunneling in real world Scanning tunneling microscope (STM): how QM tunneling lets us map individual atoms on surface Interesting example not time to cover but in notes: Sparks and corona discharge (also known as field emission) electrons popping out of materials when voltage applied. Many places including plasma displays.

21 warm up on what electron does at barrier then apply If the total energy E of the electron is LESS than the work function of the metal, V 0, when the electron reaches the end of the wire, it will A. stop. B. be reflected back. C. exit the wire and keep moving to the right. D. either be reflected or transmitted with some probability. E. dance around and sing, I love quantum mechanics!

22 a more common manifestation of QM tunneling 1. understanding discharges- electrons popping out of surface when voltage applied. What electric field needed to rip electron out of solid if no tunneling? + r - + r - + r - solid + r - + r - + r - + r - Applied E must exceed E of nucleus. Using H to estimate E nuc. E ~ kq/r 2 ~ 26 V/ nm ~ 5 x V/m ~ 5 x 10 9 V/cm E V

23 so would need around 5 x 10 9 V/cm J. Travoltage sim Get few billion volts from rubbing feet on rug? NO! Electrons tunnel out at much lower voltage. d V What is the minimum we need to know to figure out tunneling probability? a. only d b. only V c. V and d d. V, d, and work functions of finger and doorknob e. none of the above, need additional information ans. d. if have these, can get potentials, solve Schrod Eqn

24 so would need around 2.6 x 10 9 V/cm J. Travoltage sim Get few billion volts from rubbing feet on rug? NO! Electrons tunnel out at much lower voltage. d Energy Work Function Of finger U d V E Potential difference between finger/door Work Function Of doorknob V = 0, T ~e -2 a tiny. Rub feet, what happens to potential energy? x Distance to tunnel much smaller. Big V a small, so e -2 a big enough, e s tunnel out!

25 energy SAMPLE METAL Book description of STM wrong. - Says looks like this, and one looks at tunneling current from sample to tip to measure gap. x tip Tip What is wrong with this? Electron tunnels from sample to tip. What would V(x) look like then? a. same as before. b. V in tip higher, V sample lower. c. V in tip lower, V sample higher. d. V same on each side as before but barrier higher. ans. b. electron piled on top (in energy) of many other electrons that contribute to V(x). Add electron, makes higher V(x), remove makes lower. So what does next electron want to do?