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December 10, 2013 7.2: Radio Astronomers Can Detect Clouds Of 현대<¬Y: December 10, 2013 숙제 7 풀t 8제 7.2: Radio astronomers can detect clouds of hydrogen in our galaxy too cool to radiate in the optical part of the spectrum by means of the 21-cm spectral line that corresponds to the flipping of the electron in a hydrogen atom from having its spin parallel to the spin of the proton to having it antiparallel. Find the magnetic field experienced by the electron in a hydrogen atom. tõ : ¤@t 같@ )¥Ð서 반대 )¥<\ 정, LX Ð너지 (t가 수소Ð자Ð서 )출되는 21-cm 파¥X [D 만들´´므\, hc ∆E = = +µ B − (−µ B) = 2µ B λ B B B 임을 손}게 L 수 있다. ø러t 우¬가 D는 값<\부0 자0¥ B| lXt D래@ 같@ 값D »D 수 있다. hc B = = 0:051 T 2µBλ 1 8제 7.5: Protons and neutrons, like electrons, are spin- 2 particles. The nuclei of ordinary helium 4 atoms, 2 He, contain two protons and two neutrons each; the nuclei of another type of helium 3 4 atom, 2 He, contain two protons and one neutron each. The properties of liquid 2 He and liquid 3 2 He are different because one type of helium atom obeys the exclusion principle but the other does not. Which is which, and why? 4 tõ : 전´ ¤@D Ä산t보t, 짝수개X 반정수 ¤@ 입자\ l1된 2 He@ 반드시 정수X ¤@D 3 가8| X므\ 보tt 되고 @수개X 반정수 ¤@ 입자\ l1된 2 He @ 반정수X ¤@D 가8| 3 X므\ 페tø(t 된다. 파¸¬X 0타Ь는 페tø(Ð만 적©되므\ 2 He@ 0타Ь| 다t게 된다. 8제 7.8: What is true in general of the properties of elements in the same period of the periodic table? Of elements in the same group? tõ : 같@ 주0X Ð소들@ 전자의 ÍÈ lp가 같0 L8Ð l조적@ 1È@ D·X다. ø러나 전자의 lpÐ 0|서 Î@ 1È들t 달|지0 L8Ð õ통적x 1È@ 0\ >0 ´5다. 다만 같@ øùX Ð소들@ \x각 전자 lp가 n만 다| Ð, D전히 같0 L8Ð TY적<\ I¥히 D·X다. 8제 7.12: Verify that atomic subshells are filled in order of increasing n + l, and within a group of given n + l in order of increasing n. 1 현대<¬Y: December 10, 2013 tõ : 8제Ð 주´Ä 것처럼, n + lX 순서\ 전자 ÍÈD 나열t보Ä] X자. n + l 전자 ÍÈ nt 증가X는 순서\ 정, n + l = 1 1s 1s n + l = 2 2s ! 2s n + l = 3 3s 2p ! 2p ! 3s n + l = 4 4s 3p ! 3p ! 4s n + l = 5 5s 4p 3d ! 3d ! 4p ! 5s n + l = 6 6s 5p 4d ! 4d ! 5p ! 6s n + l = 7 7s 6p 5d 4f ! 4f ! 5d ! 6p ! 7s n + l = 8 8s 7p 6d 5f ! 5f ! 6d ! 7p ! 8s 위의 순서는 Figure 7.12@ 정U히 |XX므\ 8제Ð 주´Ä 것과 같t n + lt 증가X는 )¥<\ 전자 ÍÈÐ 전자가 (게 되고 같@ n + l중Ð서는 nt 증가X는 순서\ 전자가 (á(á 쌓t게 된다. 8제 7.13: The ionization energies of Li, Na, K, Rb, and Cs are, respectively, 5:4, 5:1, 4:34, 4:2, and 3:9eV . All are in group 1 of the periodic table. Account for the decrease in ionization energy with increasing atomic number. tõ : ¨든 Ð소는 수소@ 같@ 형태\ n번ø sXÐ 전자| X나 가지고 있으p Ð소 번8가 커ÐÐ 0|서 \x각 전자는 점점 @´지게 된다. 각각X ½우 \x각 전자의 위X는 1s부0 5sÐ 위XX게 되므\ Ð자 uÐ Xt 작©X는 전자0%t }t8서 점점 T }게 t(T가 가¥tÄ다. 8제 7.14: The ionization energies of the elements of atomic numbers 20 through 29 are very nearly equal. Why should this be so when considerable variations exist in the ionization energies of other consecutive sequences of elements? tõ : Ð소 번8 20번부0 29번L지X Ð자들@ \x각전자\ 4sXD 가지고 있다. t ½우Ð t (T Ð너지는 Effective nuclear chargeÐ XtX게 되는p, 대´\ Ð소 번8가 X나) ,|감Ð 0|서 양1자@ 전자가 X나) 증가X0 L8Ð pX D·\ 전X| 가지게 되고, \x각 전자가 같@ XÐ t¬X여 p¬가 D·X0 L8Ð D·\ t(T Ð너지| 가지게 된다. 8제 7.16: The effective nuclear charge that acts on the outer electron in the sodium atom is 1:84e. Use this figure to calculate the ionization energy of sodium. tõ : Effective nuclear charge가 Zet고 \x각 전자의 주양자수가 n| L, Z2E 1:842E E = 1 = 1 = −5:12eV n n2 9 t므\ t(T Ð너지는 5:12eV 가 된다. 8제 7.17: Why are Cl atoms more chemically active than Cl− ions? Why are Na atoms more chem- ically active than Na+ ions? tõ : ClX ½우Ð는 가¥ 바eX XÐ 전자가 X나 부qX고 NaX ½우Ð는 가¥ 바eX XÐ 전자가 X나만 t¬\다. |반적<\ Ð자는 \x각Ð 전자가 ÆD ½우Ð Ð자의 effective 전X량 t ®D8서 다x <È과X 반QD ¼¬게 된다. t러\ t \ Cl@ X나X 전자| 받D서, Na는 X나X 전자| 버$서 Cl−@ Na+가 되´ 보다 H정적t게 된다. 2 현대<¬Y: December 10, 2013 8제 7.18: Account for the general trends of the variation of atomic radius with atomic number shown in Fig. 7:11. tõ : |반적<\ 같@ 주0X Ð소들@ 1qt 가¥ p l0| 가지게 되고 Ð소 번8가 X나) ,| 갈수] 점점 작D지게 된다. t 는 전자의 X@ ø대\t지만 양1자의 수는 증가X여 전자0%t 강t지0 L8Ð Ð자의 l0가 점점 작D지는 것t다. ø러나 주0가 커È수] Ð자| l1X는 양1자@ 전자의 +자가 ÎD지0 L8Ð T < 전자ÍÈL지 전자가 (게 되고, 또\ 양1자가 너4 ÎD8서 l0가 커지므\ 높@ 주0X Ð소| 수] 작은 주0X Ð소Ð Dt서 커지게 된다. 8제 7.21: Why is the normal Zeeman effect observed only in atoms with an even number of electrons? tõ : 전´ ¤@t 0t 되´|만 normal Zeeman effect가 관0되고 ø렇지 J@ ½우Ð는 anoma- lous Zeeman effect가 관!된다. ø러므\ 전´ ¤@t 0t 되는 ½우| 위t서는 짝수개X 전자가 있´|만 \다. 8제 7.22: Why is the ground state of the hydrogen atom not split into two sublevels by spin-orbit coupling? tõ : Ground stateÐ서는 전자가 1s XÐ t¬X고 t LX ¤@@ 1/2, 각´동량@ 0t 된다. ø러t 가¥\ 전´ 각´동량X 값t 1/2밖ÐÆ0 L8Ð spinX orientation@ X나밖Ð t¬X지 J고 t L8Ð singlet t 된다. 8제 7.24: An atom has a single electron outside closed inner shells. What total angular momentum J can the atom have if it is in a P state? In a D state? tõ : H½X X들@ 각´동량과 ¤@t 0t 되므\ 가¥ 바eX 전자만 고$Xt 된다. <저 ¤@@ 전자 X나X ½우t므\ 1/2가 되고, 각´동량@ 전자가 P stateÐ 있으t 1, D stateÐ 있으t 2가 된다. ø러므\ 각각X ½우Ð 대t서 전´ 각´동량 J는 P stateÐ 대t서 3/2, 1/2t 가¥X고 D stateÐ 대t서 5/2, 3/2t 가¥X다. 8제 7.26: (a) What are the possible values of L for a system of two electrons whose orbital quantum numbers are l1 = 1 and l2 = 3? (b) What are the possible values of S? (c) What are the possible values of J? tõ : (a) Lt 가¥\ 값@ jl1 − l2j부0 l1 + l2L지 가¥X므\ 2, 3 ø¬고 4가 수 있다. (b) 각 전자의 ¤@@ 1=2t므\ L과 같@ 방법<\ Ä산Xt S는 0과 1 t 가¥X다. (c) t제 전´ 각´동량 J 또\ 위@ ¬\ 방법<\ jL − Sj부0 L + SL지 가¥X므\, 0, 1, 2, 3, 4, ø¬고 5가 가¥X다. 8제 7.30: The magnesium atom has two 3s electrons outside filled inner shells. Find the term symbol of its ground state. tõ : <저 전자가 n = 3x XÐ t¬\다. ø¬고 sXÐ 있0 L8Ð 각 전자의 각´동량 l = 0 t고 t L8Ð 각´동량 L@ 손}게 0t (D L 수 있다. 또\, 각 전자의 ½우Ð는 s = 1=2t므\ 가¥\ ¤@ S는 0과 1xp, P 전자가 같@ )¥X ¤@D 가지지 JD| X는 0타ЬРXt 서 자동적<\ 0t 된다. ø러t J는 가¥\ ½우가 0밖ÐÆ다. t제 term symbol\ 나타´보t, D래@ 같다. 1 ground state of magnesium = 3 S0 3 현대<¬Y: December 10, 2013 8제 7.32: In a carbon atom, only the two 2p electrons contribute to its angular momentum. The 3 ground state of this atom is P0, and the first four excited states, in order of increasing energy, 3 3 1 1 are P1, P2, D2, and S0. (a) Give the L, S, and J values for each of these five states. (b) Why 3 do you think the P0 state is the ground state? tõ : (a) 8제| 풀t서, S > Lx지 D닌지Ð 0|서 multiplicity가 달|Ä다는 점Ð XX여 잘 ´´보Ä] Xt, LSJ 3 P0 1 1 0 3 P1 1 1 1 3 P2 1 1 2 1 D2 2 0 2 1 S0 0 0 0 위@ 같t 각각X ½우Ð 대\ 값들D »D 수 있다. (b) 전자의 l1D ´´보t 전자의 자0¨X¸ 값t 각각 1=2| tè는, 즉 같@ )¥<\ 전자의 ¤@t 0열되´ Ð너지가 ®@ Á태가 되는 H정적x Á태는 3P 임을 손}게 L 수 있다. 다만 3 여0Ð서 전´ 각´동량t 작을수] 다x 입자Ð Xt서 받는 영¥t 적0 L8Ð P0가 ground state | 것t다. 2 8제 7.33: Why is it impossible for a 2 D3=2 state to exist? tõ : 8제Ð서 주´Ä Áit ground state|고 가정X자. ø러t D는 LX 값t 2임을 L$주고, 또\ multiplicity가 2 |는 점Ð서 S 는 1=2 임을 L 수 있다. ø런p, n = 2| L, Lt 2가 되는 전자 lp는 t¬X지 J0 L8Ð 주´Ä Ái@ »´È 수가 Æ다. \ÐXt 가¥\ ground state X 전자 l1@ n = 2| L, 2si, 2pjt고 t L, i는 1과 2, j는 1부0 6L지 가¥X다. ¨든 ½우Ð 대t서 L@ 0 DÈt 1t0 L8t다. 2 8제 7.38: The ground state of chlorine is P3=2. Find its magnetic moment (see previous exercise). Into how many substates will the ground state split in a weak magnetic field? tõ : Term symbol\부0, S는 1=2, L@ 1, ø¬고 J는 3=2t다.
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