Quantum tunneling: α-decay

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1 Announcements: Quantum tunneling: α-decay Exam 2 solutions ae posted on CULean Homewok solutions will be posted by 7pm tonight Next weeks homewok will be available by noon tomoow Homewok aveage fo set 9 was 36. I hope to have the exams gaded by class on Fiday. Physics 2170 Sping

2 Quantum bound state simulation The quantum bound state simulation can be used to figue out and visualize wave functions and pobabilities fo vaious potential cuves. Physics 2170 Sping

3 On to quantum tunneling The thinne o shote the baie, the easie it is to tunnel Enegy E paticle V=0 ev 0 L x Examples: Electon in wie going though ai gap (Tutoial) Alpha decay: Explained by Gamow and seen in smoke detectos, adon, space pobe powe, and assassinations Scanning tunneling micoscope Getting shocked just befoe touching the doo knob Physics 2170 Sping

4 Clicke question 1 If the total enegy E of the electon is less than the wok function of the metal, V 0, when the electon eaches the end of the wie, it will Set fequency to DA Enegy V(x)=V 0 V(x)=0 0 E x A. stop. B. be eflected back. C. exit the wie and keep moving to the ight. D. eithe be eflected o tansmitted with some pobability. E. dance aound and sing, I love quantum mechanics! Quantum mechanics is not so weid that the electon can keep taveling foeve with E<V 0. This scenaio is called a potential step (the baie goes on foeve). Physics 2170 Sping

5 Electon encountes potential step Real( ) Electon can penetate into the baie, but is eflected eventually. Tansmitted means continues off to the ight foeve, i.e. the wave function does not go down to zeo. Physics 2170 Sping

6 Quantum tunneling L If the potential incease has a finite width, it is a potential baie and the electon can tunnel out of Region I Real( ) This is what you wee encouaged to deive in the tutoial L Coppe wie #1 CuO Coppe wie #2 Physics 2170 Sping

7 Quantum tunneling pobability The pobability of tunneling depends on two paametes: 1. The paamete α measues how quickly the exponential decays and λ=1/α is the penetation depth (how fa the wave function penetates). 2. The width of the baie L measues how fa the paticles has to tavel to get to the othe side. ( V E) α = 2m h The quantum tunneling pobability is P e 2αL L As α inceases (penetation depth deceases), pobability deceases. As L inceases (baie width inceases), pobability deceases. L Physics 2170 Sping

8 Quantum Tunneling Sim Physics 2170 Sping

9 Radon-222: 86 potons, 136 neutons Radioactive decay Poton (positive chage) Neuton (no chage) Two competing foces act inside the nucleus: Coulomb foce: Potons have the same chage and ae vey close togethe so thee is a lage epulsion fom the Coulomb foce. Nuclea foce: Potons and neutons feel the stong foce which is a vey stong attactive foce but vey shot ange. Nuclei with many potons and neutons ae geneally unstable. One type of adioactive decay is called alpha decay which eleases an α paticle) Alpha paticle is 2 neutons + 2 potons (Helium nucleus) Physics 2170 Sping

10 Poton (positive chage) Neuton (no chage) Radon potons, 136 neutons Radioactive decay In alpha-decay, an alpha-paticle is emitted fom the nucleus. The aises the atio of neutons to potons Since neutons ae neutal, thee is no Coulomb epulsion. Thus, inceasing the neuton to poton atio makes a moe stable nucleus. Physics 2170 Sping

11 Analyzing alpha decay Stating point always to look at potential enegy cuve fo paticle Nucleus (Z potons & bunch o neutons) + New nucleus Alpha paticle (Z-2 potons & (2 potons & bunch o neutons) 2 neutons) Look at this system as the distance between the alpha paticle and the nucleus changes. As we bing the α paticle close, what happens to the potential enegy? Answeing this question will help us figue out the potential enegy cuve. (Z-2) Fa away, V=0 Physics 2170 Sping

12 Clicke question 2 Set fequency to DA Fa away, V=0 As α paticle gets close, what happens to the potential enegy? Which is the best epesentation of the potential enegy? kq q2 V( ) = = nucleus k( Z 1 α 2)( e)(2e) A B V() V() Takes enegy to push positively chaged α towads positively chaged nucleus, so potential enegy must incease. C V() D. Something else Physics 2170 Sping

13 Coulomb &Nuclea V() 30 MeV V Bing alpha-paticle close Coulomb foce dominates kq q2 ( ) = = k( Z 1 2)( e)(2e) Enegy Edge of the nucleus (~8x10-15 m), Nuclea (Stong) foce stats acting Stong attaction between nucleons Potential enegy dops damatically Physics 2170 Sping