Name: Date: Atomic Pysics 4 1. Te de Broglie wavelegt associated wit a car movig wit a speed of 0 m s 1 is of te order of A. 10 38 m. B. 10 4 m. C. 10 4 m. D. 10 38 m.. Te diagram below sows tree eergy levels of a certai atom. 0 5.0 ev T S 15.0 ev Te poto associated wit te eergy cage T as frequecy f T ad te poto associated wit te eergy cage S as frequecy f S Te ratio f f S T is 1 A.. 3 1 B.. C.. D. 3. 1
3. A beam of electros of uiquely defied wavelegt λ is icidet o a aperture of eigt d. Te beam is travelig alog te x directio. Te eigt d is of te same order as λ. After passig troug te aperture, te compoet of mometum i te x directio is p x ad te compoet i z te directio is p z. Wic of te followig sows te ucertaity i p x ad te ucertaity i p z? p x p z A. 0 0 B. 0 C. D. 4πd πd 4πd 4 4πd 0 4. Tis questio is about te Heiseberg ucertaity priciple. A beam of electros is icidet ormally to te plae of a arrow slit as sow below. slit beam of electros x Te slit as widt x equal to 0.01 mm. As a electro passes troug te slit, tere is a ucertaity x i its positio. Calculate te miimum ucertaity p i te mometum of te electro.......... ()
(b) Suggest, by referece to te origial directio of te electro beam, te directio of te compoet of te mometum tat as te ucertaity p.... (Total 3 marks) 5. Tis questio is about a model of te atom. Te Scrödiger model of te atom pictures electros as clouds of egative carge surroudig te ucleus. Te distributio of carge ad mass ca be represeted by a tree-dimesioal stadig wave. Idetify te feature of te stadig wave tat gives te probability of fidig te electro at a particular positio. () A electro of mass m i a atom as total eergy E, potetial eergy E P ad kietic eergy E K. (b) Write dow expressios for (i) te relatio betwee E, E P ad E K. =(ii) te mometum p of te electro i terms of E K. (iii) te associated wavelegt λ of te electro i terms of its total eergy E. () (Total 6 marks) 6. Tis questio is about models of te ydroge atom. Te Bor model provides a partially successful explaatio of te spectrum of te ydroge atom. Te model predicts tat te eergy, E, of te electro i te ydroge atom is give by E =.18 10 18 were is a iteger ad E is i joules. 3
(i) By referece to tis equatio, describe ow te Bor model accouts for te lie spectrum of te ydroge atom. (4) (ii) Calculate te sortest wavelegt of ligt i te spectrum of atomic ydroge. () (iii) State oe caracteristic of te spectrum of atomic ydroge wic caot be accouted for by te Bor model. (b) Outlie by referece to positio ad mometum ow te Scrödiger model of te ydroge atom is cosistet wit te Heiseberg ucertaity priciple. (Total 10 marks) 4
7. Tis questio is about te Bor model of te ydroge atom ad te extesio of te model to iclude sigly ioized elium. I is teory of te ydroge atom, Bor refers to stable electro orbits. State te Bor postulate tat determies wic stable orbits are allowed. (b) Describe ow te existece of suc orbits accouts for te emissio lie spectrum of atomic ydroge. Te Bor model of te ydroge atom ca be exteded to sigly ioized elium atoms. Te model leads to te followig expressio for te eergy E of te electro i a orbit specified by te iteger. E = k were k is a costat. I te spectrum of sigly ioized elium, te lie correspodig to a wavelegt of 36 m arises from electro trasitios betwee te orbit = 3 to te orbit =. (c) Deduce te value of te ioizatio eergy of sigly ioized elium atoms. (4) 5
(d) Outlie ow te Scrödiger model of te ydroge atom leads to te idea of discrete electro eergy levels. () (Total 10 marks) 8. Tis questio is about models of te ydroge atom.i 1913 Niels Bor developed a model of te ydroge atom wic successfully explaied may aspects of te spectrum of atomic ydroge. State oe aspect of te spectrum of atomic ydroge tat Bor s model did ot explai. Bor proposed tat te electro could ave oly certai stable orbits. Tese orbits are specified by te relatio mvr = wit = 1,, 3... π were m is te mass of te electro, v its speed, r te radius of te orbit ad te Plack costat. Tis is sometimes kow as Bor s first postulate. (b) State te oter postulate proposed by Bor. () By usig Newto s secod law ad te Coulomb law i combiatio wit te first postulate, it ca be sow tat r = 4π mke were k = 1 4πε. 0 It ca also be sow tat te total eergy E of te electro i a stable orbit is give by ke E =. r 6
(c) Usig tese two expressios, deduce tat te total eergy E may be give as K E = were K is a costat. (d) State ad explai wat pysical quatity is represeted by te costat K. () (e) Outlie ow te Scrödiger model of te ydroge atom leads to te cocept of eergy levels. () (Total 10 marks) 7
9. Tis questio is about a model of te atom. Niels Bor developed a model of te ydroge atom i wic a electro of mass m ad carge e orbits a statioary proto. Te radius of te orbit is r, as sow below. ot to scale v proto (+ e) electro ( e) r Te speed v of te electro may be sow to be give by te expressio v = e. πε rm 4 0 Idetify te symbol ε 0 i te above equatio....... (b) (i) State Bor s assumptio relatig to agular mometum. () (ii) Use tis assumptio to deduce tat te radius r is give by ε 0 r = πme were is a positive iteger. 8
(c) Use te expressio i (b) (ii) to calculate, for = 1, a umerical value for r. Commet o your aswer............. (d) State oe reaso wy te Bor model ca be applied successfully oly to te ydroge-like atom....... (Total 10 marks) 9