Davisson Germer experiment Announcements:

Transcription

1 Davisson Grmr xprimnt Announcmnts: Homwork st 7 is du Wdnsday. Problm solving sssions M3-5, T3-5. Th 2 nd midtrm will b April 7 in MUEN E0046 at 7:30pm. BFFs: Davisson and Grmr. Today w will go ovr th Davisson-Grmr xprimnt. Physics 2170 Spring

2 Particls with mass can also hav a wavlngth For photons w know how to rlat momntum and wavlngth Combind (and provn by Compton ffct): p = h γ / d Brogli proposd th sam rlationship for massiv particls Th d Brogli wavlngth: λ = h / p λ Supposing th hydrogn atom lctron is a standing wav with this wavlngth lads to quantization of angular momntum and nrgy in agrmnt with th Bohr modl. But w want mor proof that an lctron is a wav. Physics 2170 Spring

3 Two slit intrfrnc with light Huygn s Principl: wavs sprad as sphrical wavs. Physics 2170 Spring

4 Doubl-slit xprimnt L bright 0.5 mm =d θ r 1 r 2 H r = r 2 -r 1 r = mλ (whr m=1,2,3 ) bright d θ θ 1 θ 2 Scrn far away so θ 1 ~θ 2 ~θ & small angl approx: sinθ=θ r = d sinθ = dθ = mλ bright H = L sinθ = Lθ H = mlλ d Physics 2170 Spring

5 Doubl-slit xprimnt L r 1 r 2 H 5 x10-4 m = d θ r = r 2 -r 1 r = mλ (whr m=1,2,3 ) r = mλ = d sinθ = dθ = mλ Calculating th pattrn for light m = 1, λ = 500 nm, so angl to first bright θ = λ/d = 500 x 10-9 /(5 x 10-4 ) = rad if L = 3 m, thn H = 3 m x = 3 mm. H = Lθ So what will th pattrn look lik with lctrons? Physics 2170 Spring

6 Enrgy and momntum rlationships Masslss particls (photons): Visibl light photons: E = pc = hc / λ 19 E = 2.5 V = J p = E / c = h / λ λ = h / p = hc / E p = V/ c = kg m/s v 8 = c = 3 10 m/s λ = 500 nm Massiv particls (lctrons): p K = 2 mv = = 2 2m 2 λ p = 2mK = h / λ λ = m h h / p = h / 2mK p Low nrgy lctrons: 18 K = 25 V = J = V/ c = kg m/s 6 v = 3 10 m/s = 0.01c λ = 0.25 nm Physics 2170 Spring

7 Clickr qustion 1 St frquncy to DA Th lowst nrgy (usful) lctrons ar around 25 V. W just found ths lctrons hav a wavlngth of 0.25 nm. If w us th sam two slits as for visibl light (d = 0.5 mm), how far apart ar th m=0 and m=1 maxima on a scrn 3 m away? A. 3 mm r = mλ =d sinθ = dθ = mλ H = L sinθ = Lθ B. 1.5 mm C.3 µm (3 m)(1)(0.25 nm) D.1.5 µm H = Lmλ = = 1.5 µ m E. 3 nm d 0.5 mm Th wavlngth of ths lctrons (0.25 nm) is 2000 tims smallr than visibl light (500 nm) so th angl and intrfrnc spacing is 2000 tims smallr for th sam slit spacing. This is too small to s. Nd slits that ar much closr. Clu coms from X-ray diffraction Physics 2170 Spring

8 Using atoms for slits Brilliant ida: Two slits ar just two sourcs. Hard to gt two sourcs th siz of an atom. Easy to gt two objcts that scattr lctrons that ar th siz of an atom! Physics 2170 Spring

9 Using atoms for slits It is difficult to gt just two atoms nxt to ach othr. But multipl qually sparatd atoms ar asy (crystal lattic) and work vn bttr. Just lik rflction diffraction grating discussd for X-ray diffraction. Physics 2170 Spring

10 Davisson Grmr xprimnt Intrfrnc from lctron scattring off vry clan nickl surfac. Ni dt. lctrons scattr off nickl atoms mov dtctor around and s what angl lctrons com off Physics 2170 Spring

11 Davisson Grmr rsults dt. Plot th rsults for numbr of lctrons vrsus scattring angl and find A pak! # s Ni scatt. angl θ So th probability of finding an lctron at a particular angl is dtrmind by th intrfrnc of d Brogli wavs! Physics 2170 Spring

12 Clickr qustion 2 To furthr prov th d Brogli wav hypothsis, thy incrasd th lctron nrgy. If d Brogli s thory is corrct, what will happn? A. Th pak will gt largr B. Th pak will gt smallr C.Th pak will shift to smallr angl D.Th pak will shift to largr angl E. Nothing will happn. St frquncy to DA # s λ = h / 0 p 50 0 scatt. angl θ d θ = mλ Incrasing nrgy incrass momntum which dcrass th angl θ = m λ = d mh pd θ Davisson Grmr trid this as wll and it workd. 1/p Physics 2170 Spring

13 Mor on mattr wavs Two slit intrfrnc has bn sn with lctrons, protons, nutrons, atoms, and in just th last dcad with Buckyballs which hav 60 carbon atoms. Elctron diffraction, lik X-ray diffraction can b usd to dtrmin th crystal structur of solids Points com from a rgular crystal. Rings com from many crystals randomly arrangd. Physics 2170 Spring

14 Elctron microscop Microscops limitd by th wavlngth of light so visibl light microscops cannot rsolv objcts < 500nm. Elctrons hav much smallr wavlngths so gt bttr rsolution from lctron microscops. Scanning lctron microscop rflcts off th surfac (for xampl of snow flaks) A Transmission lctron microscop snds lctrons through thin sampls Physics 2170 Spring