Topic Topic 12 – Quantum and nuclear physics Assessment NAME: PROBLEM SET ____________________________ ________________________________ ____ TEAM:__
Formative
THIS IS A PRACTICE ASSESSMENT. Show formulas, substitutions, answers, and units!
Topic 12.1 - The interaction of matter with raiation The followin uestions are about "hotosensiti#e metals. 1. What does does it mean mean when we say that that a metal metal is photosens photosensitie itie! !
2. What are are the electrons electrons called called that are are emitted "y "y a photosensiti photosensitie e metal! #. What is monoc monochro hromat matic ic li$ht li$ht! ! %. &n the $raph $raph to the ri$ht ri$ht la"el la"el the cuto' cuto' olta olta$e( $e( and e)plain how it is determined.
The followin uestions are about the "hotoele$tri$ "hotoele$tri$ e%e$t. *. What What is is a phot photon on! ! Photoele$tri$ E%e$t &bser#ations
+. ,omple ,omplete te the the ta"le ta"le to to the ri$h ri$ht: t: -. What What doe oes s Ip stand or! /. E)p E)plain ain the conc oncept ept o the the cuto uto' re0uency.
. ow does does the the conce concept pt o the phot photon on e)plain 13 in the ta"le!
14.ow does the concept o the photon e)plain 23!
13 Ip is proportional to the li$ht7s intensity. 23 Ip is 8ero or low enou$h cuto' re0uency f 4 re$ardless o the intensity o the li$ht. #3 Ip is o"sered immediately een with a low intensity o li$ht a"oe the cuto' re0uency f 4. %3 E9 is is independent o intensity o li$ht. *3 E9 is is dependent on re0uency o li$ht.
11.ow does the concept o the photon e)plain #3! 12.ow does the concept o the photon e)plain %3! 1#.ow does the concept o the photon e)plain *3!
E'"lained b( $lassi$al wa#e theor() 5es 5es 6 No
1%.What is a wor unction! 1*.&n 1*.&n the mathem mathemati atical cal ormul ormulati ation on o the photoe photoelec lectri tric c e'ect( e'ect( hf ; φ < E9(ma) descri"e what each part o the e0uation represents( in terms o wor and ener$y. ener$y. 1+.=escri"e and e)plain an e)periment to test the Einstein model o the photoelectric e'ect. &nclude a setch o the apparatus.
The followin uestions are a""li$ations of the "hotoele$tri$ "hotoele$tri$ e%e$t. 1-.A photos photosens ensiti itie e metal metal has a wor wor uncti unction on o #.-* #.-* e>. e>. ?ind the minimum minimum re0uency o li$ht needed to ree an electron rom its surace.
1/.& a photon hain$ a hi$her re0uency than the one determined in the preious pro"lem stries the metal( where will the e)cess ener$y $o! 1.A photosensitie metal has a wor unction o #.-* e>. e>. ?ind the ma)imum inetic ener$y o an electron reed "y a photon hain$ a re0uency o 2.*4 ×141+ 8.
The followin uestions are about matter wa#es. 24.What is meant "y the term @waeparticle dualityB and to what is it applied!
21.What is a matter wae! 22.Ctate the de Dro$lie hypothesis( and then write its mathematical ormula.
2#.resent an outline o the =aissonFermer e)periment and how it eriGed the de Dro$lie hypothesis.
The followin uestions are a""li$ations of the de *rolie h("othesis. 2%.An electron is accelerated rom rest throu$h a potential di'erence o 2-* >. What is its e)pected de Dro$lie waelen$th!
2*.A particle has an ener$y E and an associated de Dro$lie waelen$th λ . Chow that the ener$y E is proportional to λ 2.
The followin uestions are about the stru$ture of the atom. 2+.Hutline a la"oratory procedure procedure or producin$ and o"serin$ atomic spectra.
2-.E)plain how atomic spectra proide eidence or the 0uanti8ation o ener$y in atoms.
+or the followin uestions refer to the diaram to the riht. 2/.Wha 2/.Whatt is the the re0 re0ue uenc ncy y o a +*+ +*+ nm hydr hydro$ o$en en emission spectrum line!
2.What is the ener$y in I and e> o the photon rom 2/! #4.What are the ener$y leels associated with this photon!
The follow followin in uest uestion ions s $o#er $o#er deri#a deri#atio tions ns leadin leadin u" to the *ohr *ohr model model of the h(droen atom. #1.Jsin$ ,oulom"7s ,oulom"7s law or a proton and an electro electron n and the act that this orce is 2 2 centripetal in nature( show that m# ; e -r or or an electron with or"ital radius r .
#2.Jsin$ the results rom #1 and the deGnition o mechanical ener$y E ; E9 < E( show show that that the total total mechan mechanica icall ener$ ener$y y o a hydro hydro$en $en atom is $ien "y E ; – 2 K1623e -r .
The followin uestions are about the *ohr model of the h(droen atom. ##.What assumptions did Dohr mae when deelopin$ his theory o the structure o the hydro$en atom!
#%.Write the relationship "etween an$ular momentum and momentum " ; m# or or an electron or"itin$ a hydro$en nucleus at a radius o r .
#*.Write the assumption Dohr made or an$ular momentum in ormulaic orm. #+.Jsin$ your results rom #1 and #* show that r n ; n2h2 - K%π2e2m3.
#-.Now usin$ your results rom #2 and #+ show that or the hydro$en atom En ; – 1#.+ - n e>. - n2 e>.
#/.E)plain the relationship "etween the ormula you Lust ound and the dia$ram in 2/.
The followin uestion is about the /ele$tron in a bo'.0 #.Chow that the allowed inetic ener$ies o an electron that resonates in a "o) o len$th is $ien "y E9 ; ; n2h2 - K /m2 3.
The followin uestions are about S$hr1diner2s wa#e euation. %4.Write Cchrdin$er7s wae e0uation here( and tal a"out its parts( in terms o inetic( potential( and total ener$y.
%1.ow is Cchrdin$ Cchrdin$er7s er7s wae e0uation e0uation similar to the electron electron in the "o) "o) e0uation e0uation you deried in #-! ow is it di'erent! %2.ow do the electron or"itals in the Cchrdin$er model di'er rom those in the Dohr model!
The followin uestions are about tunnelin. %#.E)plain radioactie decay in terms o the wae unction ψ . Jse an alpha particle in a nucleus as an e)ample.
%%.Cel %%.Cel $raitat $raitation ion on the sun produ produces ces temper temperatu ature res s in the core o a"out a"out T ; 2.#×14 9. What this means is that on aera$e( two protons can approach to with within in r ; %./ ×141# m "eore the ,oulom" orce repels them. Fien that the
stron$ orce re0uired or usion has a ran$e that is 14 to 144 times shorter( e)plain( in terms o the wae unction ψ ( how usion mi$ht still occur.
%*.ist three actors that a'ect a particle7s a"ility to tunnel. The follow followin in uest uestion ions s are are about about the the Heisen Heisenber ber un$ert un$ertain aint( t( "rin$i "rin$i"l "le e and #iolation of $onser#ation of ener(. %+.&n $eneral words( what do the two orms o the eisen"er$ uncertainty principle say!
%-.E)plain how the J allows conseration o ener$y to "e iolated. %/.An electron and a positron are created rom the oid. ,alculate how lon$ they can e)ist. What will happen when they recom"ine!
An ele$tron and a 3et 4hter are obser#ed to ha#e eual s"eeds of 566. m-s, a$$urate to within ± 6.6768. 6.6768. %.What is the minimum uncertainty in the position o the electron!
*4.What is the minimum uncertainty in the position o the Let i its mass is -*4. $!
*1.&n li$ht o these results( e)plain the eracity o the statement @the world o the small is $rainy.B
An ele$tron in an e'$ited state has a lifetime of 7.9: × ;6 ;6<= se$on se$onds ds before before it dee'$ites. *2.What is the minimum uncertainty in the ener$y o the photon emitted on de e)citation!
*#.What is the th e ma$nitude in the "roadenin$ o the re0uency o the spectral line!
The The foll follow owin in ues uesti tion on illu illust stra rate tes s a rou rouh h /"ro /"roof0 of0 of one one of the the Heis Heisen enbe ber r relationshi"s.
*%.Jse the relationship or sin$leslit di'raction and the de Dro$lie hypothesis to proe ∆ ' ∆ " ≈ h - 2. &nclude setches.
The followin two uestions e'"lore the stru$ture of the nu$leus usin the H>P. **.Jsin$ the J show that an electron cannot e)ist inside the nucleus o an atom. Assume that the diameter o the nucleus is a"out 1 ×141* m. int: int: Jse ∆ ' ∆ " ≥ h- 2π and Gnd ∆# .
*+.Jse the same techni0ue to calculate whether or not n ot a proton can e)ist there.
Topic 12.2 ! "#c$ear ph%sics The followin uestions are about the dis$o#er( of the nu$lear stru$ture of the atom. *-.=escri"e I.I. Thompson7s plum puddin$ model o the atom.
*/.What is an alpha particle and what was its role in disproin$ the plum puddin$ model o the atom!
*.E)plain the Fei$erMarsden e)periment and how its results led to the discoery o a central massie nucleus o positie char$e.
The followin uestions are about usin head
+1.=erie the ormula the ormula R4 ; 2 ?e2 - E9 α.
+2. Cuppose an alpha particle hain$ a inetic ener$y o %.44 Me> is made to approach a silicon nucleus K ? ; ; 1%3. ?ind a "allpar G$ure or the radius to the silicon nucleus. Jse the ormula R4 ; 2 ?e2 - E9 α.
+#.?ind the nuclear radius o a siler nucleus. Jse the ormula R ; R4 A ; 1.2×141* m.
16#
where R4
+%.Chow that the density o a siler nucleus is a"out ρ ; 2.#×141- $ m#.
The followin uestions are about usin di%ra$ted beams of ele$trons and neutrons to determine the nu$lear diameter. +*.A "eam o /2.4 Me> neutrons are di'racted upon passin$ throu$h a thin lead oil. The Grst minimum in the di'raction pattern is measured at 12./ °. Estimate the diameter o the lead nucleus.
++.A "eam o %44. Me> electrons are di'racted upon passin$ throu$h a thin lead oil. Jsin$ the diameter o the lead nucleus rom the preious pro"lem determine the e)pected location o the Grst minimum in the di'raction pattern.
+-.&n the e)periment o the preious pro"lem( in addition to the normal di'raction pattern( small and une)pected anomalies are also present in the pattern. E)plain how these irre$ularities mi$ht constitute eidence or an internal structure o the nucleus Kprotons and neutrons3.
The followin uestions are about de$a( "arti$les . +/.E)plain the three types o radioactie decay.
+.Which o these three types has a pretty constant ener$y o a"out % to * Me>! -4.Which -4.Which o these these resul resulted ted in the predict prediction ion o the neutrino( neutrino( and why did the neutrino need to "e present!
-1.Which o these decay types is eidence or the e)istence o nuclear ener$y leels! ow is it eidence!
The followin uestions are about nu$lear stabilit(. -2.E)plain why nuclei hain$ many protons mi$ht "e unsta"le.
-#.Why do neutrons n eutrons add nuclear sta"ility to the hi$her atomic num"ered nuclei!
The followin uestions are about the radioa$ti#e de$a( law and half
-*.=erie the relationship "etween decay constant and hallie.
-+.The hallie o a radioactie nuclide %.* ×14 y. ?ind its decay constant.
--.&n words( what is the decay constant o a nuclide! -/.ow do Cchrdin$er7s e0uation and 0uantum tunnelin$ relate to nu clear decay!
-.Hutline methods or measurin$ the hallie o an isotope.
The followin uestions are about de$a( rates. /4.=e /4.=eca cay y rate rates s are are meas measur ured ed with with a ____ ______ ____ ____ ____ ____ ____ __ and and are are meas measur ured ed in ____________.
/1.Why is the decay rate A proportional to the population o nuclides N!
The a$ti#it( "er ram of a radioa$ti#e isoto"e is 9.= disinterations "er hour at t @ 6.66 h :. disinterations "er hour at t @ =.76 h. /2.?ind the decay constant o this isotope.
/#.?ind the hallie o this isotope. /%.?ind the actiity per $ram o the isotope o at t ; ; 14. h. /*.
& the ori$inal ori$inal sample sample had a mass o o /*.4 /*.4 $( what what is its mass mass our our hallie hallies s later!
