(Kertas soalan ini mengandungi 3 soalan dalam 7 halaman yang bercetak) (This question paper consists of 3 questions on 7 printed pages)

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1 UNIVERSITI MALAYA UNIVERSITY OF MALAYA PEPERIKSAAN IJAZAH SARJANA MUDA SAINS EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE SESI AKADEMIK 2015/2016 : SEMESTER 1 ACADEMIC SESSION 2015/2016 : SEMESTER 1 SCES3332 : SPEKTROSKOPI MOLEKUL LANJUTAN ADVANCED MOLECULAR SPECTROSCOPY Dis 2015/Jan 2016 Dec 2015/Jan 2016 Masa: 2 jam Time: 2 hours ARAHAN KEPADA CALON: INSTRUCTIONS TO CANDIDATES: Kertas soalan ini mengandungi Bahagian A dan B. This paper consists of Section A and B. Jawab soalan mengikut arahan yang diberikan di dalam setiap bahagian. Question should be answered according to the instructions given in each section. (Kertas soalan ini mengandungi 3 soalan dalam 7 halaman yang bercetak) (This question paper consists of 3 questions on 7 printed pages)

2 BAHAGIAN A (70 MARKAH) SECTION A (50 MARKS) Jawab semua soalan. Answer all questions. 1. (a) Jelaskan secara terperinci prinsip operasi asas sebuah spektrometer Transformasi Fourier. Describe in detail the operation principles of a Fourier Transformation Spectrometer. (15 markah/marks) (b) Sebuah sistem molekul hipotetikal mempunyai paras tenaga E= an(n + 4), di mana n= 0, 1, 2,... dan a adalah pemalar positif. Hukum pilihan bagi peralihan berradiasi adalah Δn = ±3. Dapatkan formula untuk frekuensi serapan yang dibenarkan dalam sebutan n bawah,a dan h (pemalar Planck). A hypothetical molecular system has the energy levels E= an(n + 4), where n= 0, 1, 2,... and a is a positive constant. The selection rule for radiative transitions is Δn = ±3. Find the formula for the allowed absorption frequencies in terms of n lower, a, and h (Planck s constant). (5 markah/marks) (c) Bagi sejumlah sistem seperti dalam soalan 1(b) yang terdistribusi pada banyak paras tenaga, frekuensi peralihan serapan yang paling rendah dilihat berlaku pada 140 GHz. Carikan frekuensi peralihan serapan seterusnya. For a collection of such system in question 1(b) distributed among many energy levels, the lowest-frequency absorption transition is observed to be at 140 GHz. Find the next lowest absorption frequency. (4 markah/marks) 2/7

3 (d) Pekali Einstein A diberi oleh; di mana ν adalah frekuensi serapan, g 1 adalah kemerosotan pada paras bawah 1, g 2 adalah kemerosotan pada paras atas 2, h adalah pemalar Planck, c adalah kelajuan cahaya, ε o adalah permitiviti ruang kosong dan µ 12 adalah momen peralihan dari paras 1 ke paras 2. Pekali Einstein A juga boleh dianggap sebagai songsangan dari jangka hayat 1 τ. Anggapkan bahawa suatu elektron beralih dari orbital s ke orbital p dan kembali ke orbital s dengan jangka hayat 1.6 x 10-9 saat. Kirakan momen peralihan bagi proses pancaran ini. Sekiranya diberi bahawa cas elektron adalah x C, berapa jauhkah elektron tersebut telah bergerak? The Einstein coefficient A is given by; where ν is the frequency of absorption, g 1 is the degeneracy of the lower level 1, g 2 is the degeneracy of the upper level 2, h is the Planck s constant, c is the speed of light, ε o is the permittivity of free space and µ 12 is the transition moment from level 1 to level 2. The Einstein coefficient A can also be thought as the inverse of lifetime 1. Assuming that an electron undergoes a transition from an s τ orbital to a p orbital and decays back to the s orbital with a lifetime of 1.6 x 10-9 s. Calculate the transition moment of the emission process. Given the charge of an electron is x C, how far have the electron moved? Given: ν = x Hz; c = x 10 8 ms -1 ; h = x J s; ε o = x C 2 N -1 m -2 (10 markah/marks) 2. (a) Nyatakan hukum pilihan bagi peralihan IR dan Raman dengan mengambil kira simetri keadaan getaran yang terlibat serta operator dwipolar dan operator keboleh-herotan. State the selection rule of IR and Raman transitions considering the symmetries of the vibrational states involved and the dipole and polarizability operators. (5 markah/marks) 3/7

4 (b) Soalan ini diasaskan kepada gambarajah di atas. This question is based on the illustration above. (i) Dalam sebutan simetri rotor, apakah simetri molekul di atas? In terms of rotor symmetry, which symmetry does the above molecule belongs to? (2 markah/marks) (ii) Dapatkan momen inersia putaran bagi molekul ini pada paksi BAB dan CAC di mana R adalah jarak ikatan AC dan r adalah jarak ikatan AB. Labelkan jisim atom A, B dan C sebagai m A, m B and m C Derive the rotational moments of inertia of this molecule about the BAB and CAC axes where R is the bond length of AC and r is the bond length of AB. Label the masses of atoms A, B and C by m A, m B and m C. (6 markah/marks) (iii) (1) Sekiranya jisim C adalah sama dengan jisim B, apakah sebutan simetri rotor bagi molekul ini? Given that the mass of C is equal to B, which rotor symmetry does this molecule belong to? (2 markah/marks) (2) Sekiranya molekul yang disebutkan dalam soalan 2(b)(iii)(1) adalah SF 6, kirakan pemalar putaran untuk molekul ini. Diberi bahawa jarak ikatan S-F adalah angstrom. 4/7

5 If the molecule decribed in question 2(b)(iii)(1) is SF 6, calculate the rotational constant for this molecule. Given the bond length of S-F is angstrom. (10 markah/marks) (3) Ramalkan spektrum putaran molekul ini dengan mengira 5 garisan peralihan spektral pertama. Lakarkan spektrum tersebut. Predict the rotational spectrum of this molecule by calculating the first 5 spectral transitions. Sketch the spectrum. (8 markah/marks) Given: RAM S = 32 g/mol; RAM F = 19 g/mol; c = x 10 8 ms -1 ; h = x J s; Avogadro Number = 6.02 x mol -1 Jawab semua soalan dalam Bagagian ini. Answer all questions in this Section. BAHAGIAN B (30 MARKAH) SECTION B (30 MARKS) 3. (a) Menurut hipotesis spin elektron boleh wujud dalam dua keadaan spin (keadaan spin α dan β). Diberi tenaga elektron dalam medan magnet B ialah According to spin hypothesis electron can exist in two spin states (α and β spin states). Given that the energy of electron in a magnetic field B is E = M S g e β B, di mana M S menunjukkan keadaan spin elektron (bernilai ½ atau -½), g e adalah nilai g bagi elektron bebas, dan β adalah Magneton Bohr. Hitungkan perbezaan tenaga bagi dua keadaan spin elektron dalam medan magnet B, kemudian tunjukkan medan resonan B o diberi oleh where M S indicate the spin state of the electron (with value of ½ or -½), g e is the free electron g value, and β is the Bohr Magneton. Calculate the difference in energy of the two spin states of electrons in the magnetic field B, hence show that the resonance field is given by B o = g e β/( hν). (3 markah/marks) 5/7

6 (b) (c) Terangkan mengapa nilai-g bagi atom hidrogen dalam keadaan dasar ( 2 S), g H, adalah sama dengan nilai-g bagi elektron bebas, g e, tetapi nilai-g bagi atom oksigen dalam keadaan dasar ( 3 P 2 ), g O, adalah sangat berbeze daripada g e Explain why the g-value for hydrogen atom in the ground state ( 2 S), g H, is the same as the free electron g-value, g e, but the g-value for the ground state of oxygen atom ( 3 P 2 ), g O, is very different from g e. (4 markah/marks) Spektrum EPR bagi satu radikal yang mempunyai dua nukleus tertentu yang setara diperhatikan mengandungi lima garisan dengan nisbah keamatan 1:2:3:2:1. Apakah spin bagi nukleus ini? Lukis satu gambarajah untuk menerangkan jawapan anda. The EPR spectrum of a radical with two equivalent nuclei of a particular kind is observed to contain five lines of intensity ratio 1:2:3:2:1.What is the spin of the nucleus? Draw a diagram to illustrate your answer. (6 markah/marks) (d) Saling tindakan antara elektron tak berpasangan dan nukleus berspin yang berada dalam satu radikal akan menghasilkan spektrum EPR yang mengandungi berbilang garisan yang dikenal sebagai struktur hiperhalus. Bagi radikal yang mengandungi satu elektron takberpasangan dan satu nukleus 14 N, The Interaction between the unpaired electron with other magnetic nuclei present in a radical will give rise to multiple lines in the EPR spectrum known as hyperfine structure. For a radical containing an unpaired electron and a 14 N nucleus, (i) (ii) (iii) Tuliskan Hamiltonan spin yang lengkap bagi radikal ini. Write down the complete spin Hamiltonian for the radical. Tuliskan enam kombinasi spin yang mungkin berlaku. Write down the six possible spin combinations. Terangkan secara ringkas bagaimana kaedah perturbasi boleh digunakan untuk menentukan tenaga tertib-satu bagi setiap kombinasi spin yang diberi dalam (ii). Explain briefly how perturbation method can be used to determine the first-order energy for each of the spin combinations given in (ii). 6/7

7 (iv) Berikan aturan pilihan bagi peralihan yang dibenarkan. Give the selection rules for the allowed transitions. (v) Ramalkan bentuk spektrum EPR yang dihasilkan oleh radikal ini. Predict the form of the EPR spectrum of this radical. (10 markah/marks) (e) Pemalar pengkupelan hiperhalus bagi atom hidrogen adalah bernilai 50.6 mt. Hitungkan pemalar pengkupelan hiperhalus bagi atom deuterium, diberi g H H = x JT -1 dan g D D = x JT -1. Lakar spektrum EPR bagi satu sampel yang mengandungi atom H dan atom D yang terhasil oleh penceraian H 2 O dan D 2 O dalam 6M asid sulfurik (mengandungi H 2 O dan D 2 O) oleh irradiasi-γ. The hyperfine coupling constant for hydrogen atom is 50.6 mt. Calculate the hyperfine coupling constant for deuterium atom, given that g H H = x JT -1 and g D D = x JT -1. Draw the EPR spectrum of a sample containing H and D atoms produced by the breakdown of H 2 O and D 2 O following the -irradiation of 6M sulphuric acid (contains H 2 O and D 2 O). (7 markah/marks) TAMAT END 7/7

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