Davisson Germer experiment

Transcription

1 Announcmnts: Davisson Grmr xprimnt Homwork st 5 is today. Homwork st 6 will b postd latr today. Mad a good guss about th Nobl Priz for 2013 Clinton Davisson and Lstr Grmr. Davisson won Nobl Priz in Grmr didn t! No dynamit mony! Today w will go ovr th Davisson-Grmr xprimnt. Physics 2170 Fall

2 Lstr Grmr Born on Octobr 10, 1896, graduatd from Cornll Univrsity in Aftr graduation h joind Bll Labs and thn srvd in World War I as a fightr pilot, arning a citation from Gnral Prshing. Aftr th war h rturnd to Bll Labs and finishd his Ph.D. at Columbia Univrsity in At Bll Labs, Grmr initially workd as an assistant to Clinton Davisson. In April of 1925 Davisson and Grmr bgan working on an xprimnt studying th diffraction of lctrons off of a nickl surfac. At first thir rsults wr similar to rsults obtaind four yars arlir. Thn suddnly th rsults changd. Physics 2170 Fall

3 Grmr cont. Thy prformd a similar xprimnt in 1927, aftr Davisson had attndd a confrnc whr DBrogli's hypothsis about th wav natur of mattr was prsntd. Whn lctrons of known vlocity wr usd to bombard th nickl surfac at a 45 dgr angl thy obsrvd that th diffraction of th lctrons obyd Bragg's Law. This was th first proof of DBrogli's particl wav hypothsis. Aftr this xprimnt Grmr continud working at Bll Labs, studying th us of this tchniqu to dtrmin th structur of surfacs, work that vntually ld to th dvlopmnt of th lctron microscop. Physics 2170 Fall

4 Particls with mass can also hav a wavlngth For photons w know how to rlat momntum and wavlngth Combind (and provn by Compton ffct): d Brogli proposd th sam rlationship for massiv particls Th d Brogli wavlngth: 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 Fall

5 Considr th difficulty Tak a small dust particl with radius, r = 10-6 m, with a dnsity, ρ, of 10 g/cm 3, and moving with a vlocity of of v = 10-2 m/s. Sinc v is much, much lss than c, W can writ p = mv = 4/3 π r 3 ρ v 4 x kg m/s d Brogli wavlngth is: λ= h/p = 6.63 x J s/ 4 x kg m/s = 1.6 x m This is xtrmly small compard to th dimnsions of any physical systm. Elctron s mass is rally small and that hlps in incrasing th wavlngth. Physics 2170 Fall

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

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

8 Doubl-slit xprimnt L r 1 r 2 H 5 x10-4 m = d θ Δr = r 2 -r 1 Δr = mλ (whr m=1,2,3 ) Δr = 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 Fall

9 Enrgy and momntum rlationships Masslss particls (photons): Visibl light photons: Massiv particls (lctrons): Low nrgy lctrons: Physics 2170 Fall

10 Clickr qustion 1 St frquncy to AD 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 B. 1.5 mm C. 3 µm D. 1.5 µm E. 3 nm Δr = mλ = d sinθ = dθ = mλ H = L sinθ = Lθ Physics 2170 Fall

11 Clickr qustion 1 St frquncy to AD 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 B. 1.5 mm C. 3 µm D. 1.5 µm E. 3 nm Δr = mλ = d sinθ = dθ = mλ H = L sinθ = Lθ 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 Fall

12 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 Fall

13 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 Fall

14 Davison Grmr Apparatus Rgion travrsd by lctrons is vacuatd! Physics 2170 Fall

15 Davison-Grmr Rsult Physics 2170 Fall

16 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 Fall

17 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! It is an intrfrnc btwn wavs, associatd with a singl lctron, that hav bn scattrd from various parts of th crystal. Physics 2170 Fall

18 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 AD # s scatt. angl θ Physics 2170 Fall

19 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 AD # s scatt. angl θ Incrasing nrgy incrass momntum which dcrass th angl θ Davisson Grmr trid this as wll and it workd. 1/p Physics 2170 Fall

20 Mor on mattr wavs Two slit intrfrnc has bn sn with lctrons, protons, nutrons, and 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 Fall

21 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 Fall

22 Diffrnt Probs Many diffrnt microscops usd in laboratoris to invstigat matrial proprtis. Ordinary light not vry good blow 1 micron. Low nrgy lctrons usd to study surfac ffcts calld LEED Low nrgy lctron diffraction. X-rays good for lctronic structur light sourcs Nutrons usd to study crystals containing hydrogn Physics 2170 Fall

23 Wavs and Wav-Function W will start talking about wavs and a particl s wavfunction on Friday. Should rad about it In th book Physics 2170 Fall