(Kertas soalan ini mengandungi 12 soalan dalam 9 halaman yang bercetak) (This question paper consists of 12 questions on 9 printed pages)

PEPERIKSAAN IJAZAH SARJANA MUDA SAINS

EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE SESI AKADEMIK 2018/2019 : SEMESTER II

ACADEMIC SESSION 2018/2019 : SEMESTER II SID3003 : Kimia Fizik Lanjutan

: Advanced Physical Chemistry

Jun 2019 MASA: 3 jam

June 2019 TIME: 3 hours

ARAHAN KEPADA CALON:

INSTRUCTIONS TO CANDIDATES:

Kertas soalan ini mengandungi Bahagian A, B, C dan D.

This paper consists of Section A, B, C and D.

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 12 soalan dalam 9 halaman yang bercetak) (This question paper consists of 12 questions on 9 printed pages)

2/9 BAHAGIAN A (25 MARKAH)

SECTION A (25 MARKS) Jawab SEMUA soalan.

Answer ALL questions.

1. Bila fungsi variasi 𝜙 = 𝑐₁𝑓₁+ 𝑐₂𝑓₂ diguna kepada satu masalah mekanik kuantum, didapati ⟨𝑓₁|𝐻̂|𝑓₁⟩ = 4𝑎, ⟨𝑓₁|𝐻̂|𝑓₂⟩ = 𝑎, ⟨𝑓₂|𝐻̂|𝑓₂⟩ = 6𝑎, ⟨𝑓₁|𝑓₁⟩ = 2𝑏,

⟨𝑓₂|𝑓₂⟩ = 3𝑏, ⟨𝑓₁|𝑓₂⟩ = 𝑏, di mana 𝑎 dan 𝑏 adalah pemalar positif yang diketahui.

Guna 𝜙 bagi mendapatkan (daripada segi 𝑎 dan 𝑏) dua tenaga terendah.

When the variation function 𝜙 = 𝑐₁𝑓₁+ 𝑐₂𝑓₂ is applied to a certain quantum-mechanical problem, one finds ⟨𝑓₁|𝐻̂|𝑓₁⟩ = 4𝑎, ⟨𝑓₁|𝐻̂|𝑓₂⟩ = 𝑎, ⟨𝑓₂|𝐻̂|𝑓₂⟩ = 6𝑎, ⟨𝑓₁|𝑓₁⟩ = 2𝑏, ⟨𝑓₂|𝑓₂⟩ = 3𝑏, ⟨𝑓₁|𝑓₂⟩ = 𝑏, where 𝑎 and 𝑏 are known positive constants. Use this 𝜙 to find (in terms of 𝑎 and 𝑏) the lowest two energies.

(4 markah/marks) 2. Bagi helium, pembetulan tenaga pengusikan tertib pertama adalah 𝑒²/4𝜋𝜀₀𝑟₁₂

purata ke atas fungsi gelombang sebenar tidak diusikan. Tunjukkan bahawa jika nilai purata (atau jangkaan) 〈𝑒²/4𝜋𝜀₀𝑟₁₂〉 dinilai menggunakan fungsi tertib sifar yang tidak benar 1𝑠(1)2𝑝(2) atau 1𝑠(2)2𝑝(1), 𝐽_1𝑠2𝑝 diperolehi dalam setiap kes. Sekarang tunjukkan bahawa bila fungsi-fungsi sebenar diguna untuk menilai 〈𝑒²/4𝜋𝜀₀𝑟₁₂〉, 𝐽_1𝑠2𝑝± 𝐾_1𝑠2𝑝 (sebagaimana E⁽¹⁾ diperolehi daripada penentu sekular) diperolehi. Kenapa penilaian awal 〈𝑒²/4𝜋𝜀₀𝑟₁₂〉 adalah benar berbanding yang kemudian?

For helium, the first-order perturbation energy correction is 𝑒²/4𝜋𝜀₀𝑟₁₂ averaged over the correct unperturbed wave function. Show that if the average (or expectation) value

〈𝑒²/4𝜋𝜀₀𝑟₁₂〉 is evaluated using the incorrect zeroth-order function 1𝑠(1)2𝑝(2) or 1𝑠(2)2𝑝(1), 𝐽_1𝑠2𝑝 is obtained in each case. Now show that when the correct functions are used to evaluate 〈𝑒²/4𝜋𝜀₀𝑟₁₂〉, 𝐽_1𝑠2𝑝± 𝐾_1𝑠2𝑝 (as E⁽¹⁾ found from a secular determinant) are obtained. Why the latter evaluation of 〈𝑒²/4𝜋𝜀₀𝑟₁₂〉 is correct compared to the former one?

(5 markah/marks) 3. Pertimbangkan penentu Slater fungsi gelombang atom

Consider the Slater determinantal atomic wave function

Ψ = 1

√2|𝜓_2,1,1(1)𝛼(1) 𝜓_2,1,−1(1)𝛽(1) 𝜓_2,1,1(2)𝛼(2) 𝜓_2,1,−1(2)𝛽(2)|

di mana 𝜓_2,1,±1 adalah fungsi-fungsi gelombang semacam hidrogen. Jumlah komponen z momentum sudut orbital diberi oleh

where 𝜓_2,1,±1 are hydrogenlike wave functions. The total z-component of orbital angular momentum is given by

3/9 𝐿̂_𝑧 = 𝐿̂_𝑧1+ 𝐿̂_𝑧2

Dapatkan nilai eigen 𝐿̂_𝑧. Find the eigenvalues of 𝐿̂_𝑧.

(5 markah/marks) 4. Gambarajah 1 menunjukkan beberapa terma tenaga atom karbon.

Figure 1 shows some term energies of the carbon atom.

Figure 1

Bincangkan secara ringkas tenaga-tenaga kuantum mekanik yang terlibat dalam pemisahan semua terma dalam gambarajah 1. Anda boleh memberi dua atau lebih terma sebagai contoh dalam jawapan diberi. Terbitkan simbol-simbol dalam gambarajah 1 yang timbul dari konfigurasi elektronik 1𝑠²2𝑠²2𝑝3𝑝.

Discuss briefly the quantum mechanical energies involved in separating all the terms in Figure 1. You can give any of two or more terms as examples in the given answer.

Derive the symbols in Figure 1 arising from 1𝑠²2𝑠²2𝑝3𝑝 electronic configuration.

(6 markah/marks)

4/9 5. Gambarajah 2 menunjukkan lengkungan tenaga keupayaan U(R) bagi

beberapa keadaan elektronik H².

Figure 2 shows potential energy U(R) curves for some electronic states of H2.

Figure 2

Daripada prinsip pertama teori orbital molekul, bincang secara ringkas bagaimana membina lengkungan tenaga keupayaan U dan menentukan tenaga penceraian bagi keadaan electronik dasar 𝑋 𝛴¹ _𝑔⁺. Terbitkan symbol- simbol terma molekul bagi keadaan teruja elektronik 𝑏 𝛴³ _𝑢⁺ dan 𝐵 𝛴¹ _𝑢⁺ dalam gambarajah 2.

From first principle of molecular orbital theory, discuss briefly on how to construct the potential energy curve in Figure 2 and to determine the dissociation energy for the ground electronic state 𝑋 𝛴¹ _𝑔⁺. Derive molecular term symbols for the excited electronic states 𝑏 𝛴³ _𝑢⁺ and 𝐵 𝛴¹ _𝑢⁺ in Figure 2.

(5 markah/marks)

5/9 BAHAGIAN B (25 MARKAH)

SECTION B (25 MARKS) Jawab SEMUA soalan.

Answer ALL questions.

6. (a) Beri takrifan entropi statistik, S* dan bandingkan ia dengan kuantiti serupa daripada hukum termodinamik kedua.

Define the statistical entropy, S* and compare this with a similar quantity from the second law of thermodynamics.

(4 markah/marks) (b) Andaikan satu sistem yang mempunyai bilangan zarah N = 25,000,000 hanya mempunyai dua tahap tenaga dipisahkan oleh perbezaan tenaga Δε = 5.0 x 10^-21 J. Kira nisbah taburan populasi antara dua tahap tenaga pada 100 K dan pada 1,000 K. Kira suhu sistem jika tahap tenaga yang lebih tinggi mengandungi dua kali lebih banyak zarah berbanding tahap tenaga yang lebih rendah. Komen jawapan anda.

Considering a system of N=25,000,000 particles which has only two energy levels separated by energy difference of Δε = 5 x 10^-21 J. Calculate the ratio of the population distribution between the two energy levels at 100 K and at 1,000 K. If the higher energy level contains twice as many particles as the lower energy level, calculate the temperature of the system. Comment on your answer.

(8 markah/marks) (c) Suatu sistem terpencil hanya mempunyai 3 zarah (N = 3) dan jumlah tenaga, E dengan nilai 4ε. Jika lima tahap tenaga yang ada ialah 0, ε, 2ε, 3ε, 4ε:

An isolated system has only 3 particles (N = 3) and the total energy, E of 4ε. If the five available energy levels are 0, ε, 2ε, 3ε, 4ε:

(i) Beri semua konfigurasi tenaga yang mungkin Give all possible energy configurations

(ii) Kenalpasti konfigurasi dengan kebarangkalian paling tinggi Identify the configuration with the highest probability

(iii) Kira entropi bagi konfigurasi di (ii)

Calculate the entropy for the configuration in (ii)

(5 markah/marks)

6/9 7. (a) Kira fungsi sekatan putaran untuk satu molekul bukan linear yang

mempunyai simetri, σ = 3 at 25°C.

Diberi: A = 2.414 cm^-1, B = 0.508 cm^-1 and C = 0.412 cm^-1

Calculate the rotational partition function for a non-linear molecule whose symmetry, σ = 3 at 25°C.

Given: A = 2.414 cm^-1, B = 0.508 cm^-1 and C = 0.412 cm^-1

(5 markah/marks) (b) Guna teorem sekatan samarata untuk menganggarkan kapasiti haba molar bagi 𝐼₂, 𝐶𝐻₄dan 𝐶₆𝐻₆ dalam fasa gas pada 25°C, pada isipadu malar.

Use the equipartition theorem to estimate the molar heat capacity of 𝐼₂, 𝐶𝐻₄ and 𝐶6𝐻6 in the gas phase at 25°C, at constant volume.

(3 markah/marks)

7/9 BAHAGIAN C (25 MARKAH)

SECTION C (25 MARKS) Jawab SEMUA soalan.

Answer ALL questions.

8. Beri perbezaan di antara fotosistem I dan fotosistem II.

Give the differences between photosystem I and photosystem II.

(10 markah/marks) 9. Pendarflour untuk sebatian pewarna apabila didedahkan kepada sinaran

cahaya pada 350 nm dikaji dalam kehadiran ejen pemadaman. Berikut adalah keamatan cahaya yang diperoleh:

The fluorescence of a dye when it was irradiated by 350 nm light was studied in the presence of a quenching agent. The following intensities were observed:

[Q], (mmol L^-1) 1.0 2.0 3.0 4.0 5.0

𝐼_𝑓⁰ 𝐼_𝑓

⁄ 5.2 9.4 13.7 18.0 22.2

Pada siri kajian kedua, cahaya insiden dipadam dan kemerosotan cahaya pendarflour diperhatikan:

In the second series of experiments, the incident light was shut and the decay of fluorescence was observed:

[Q], (mmol L^-1) 1.0 2.0 3.0 4.0 5.0

, ns 91 51 34 25 22

Diberi penyelesaian plot Stern-Volmer:

Given the Stern-Volmer plot which has the solution:

𝐼_𝑓⁰

𝐼_𝑓 = 1 +𝑘_𝑓 𝑘_𝑞[𝑄]

Tentu kadar tindakbalas pemadaman.

Determine the quenching rate constant.

(15 markah/marks)

8/9 BAHAGIAN D (25 MARKAH)

SECTION D (25 MARKS) Jawab SEMUA soalan.

Answer ALL questions.

10. Bagaimanakah pemindahan elektron teori Marcus menerangkan bahawa adalah mungkin bagi satu tindakbalas yang mempunyai tenaga bebas besar (-ΔG) boleh menjadi lebih perlahan berbanding tindak balas yang mempunyai tenaga bebas kurang negatif. Lakar gambarajah bagi membantu penjelasan anda.

How does Marcus theory of electron transfer explain that it is possible for a reaction with a large negative free energy (−ΔG ) to be slower than one with a less negative free energy. Sketch the diagram to help on your explanation.

(8 markah/marks)

11. Teori Marcus menerangkan tindakbalas pemindahan elektron.

Marcus Theory explains the electron transfer reactions.

(Diberi:

Given:

, )

9/9 (a) ΔG ialah perubahan tenaga bebas antara reaktan di sebelah kiri dan produk di sebelah kanan, ΔE adalah tenaga pengaktifan dan λ adalah tenaga penyusunan semula. Nyatakan ΔG, ΔE, dan λ bagi gambarajah di atas.

ΔG is the free energy change between the reactants on the left and the products on the right, ΔE is the activation energy and λ is the reorganization energy. Indicate ΔG, ΔE, and λ in the graph above.

(b) Apakah makna fizikal bagi tenaga penyusunan semula?

What is the physical meaning of the reorganization energy?

(c) Apakah hubungan antara perubahan tenaga bebas dan tenaga penyusunan semula apabila pemalar kadar adalah maksimum?

What is the relationship between the free energy change and the reorganization energy when the rate constant is maximal?

(d) Pada 40°C, pemalar kadar bagi tindakbalas pemindahan elektron tertentu adalah dua kali daripada kadar pada 0°C. Dengan mengandaikan bahawa pemalar keseimbangan tindakbalas adalah kira- kira 100 (memihak kepada produk) dan tidak bersandar dengan suhu dalam julat ini, apakah tenaga penyusunan semula untuk tindakbalas ini (andaikan ΔG = ΔG° untuk tindakbalas ini)? Diberi tenaga bebas standard untuk tindakbalas adalah -11.0 kJ/mol.

At 40°C, the rate constant for a particular electron transfer reaction is twice of the rate at 0°C. Assuming that the equilibrium constant for the reaction is about 100 (favoring the product) and roughly independent of temperature over this range, what is the reorganization energy for this reaction (assume ΔG = ΔG°

for this reaction)? Given the standard free energy for the reaction is -11.0 kJ/mol.

(10 markah/marks) 12. Terbitkan persamaan yang menerangkan isoterma penjerapan Langmuir untuk

gas di permukaan. Tentukan semua kuantiti yang terlibat dan berserta unitnya.

Dapatkan ungkapan bagi pergantungan liputan permukaan pada tekanan dalam had tekanan rendah dan tinggi.

Derive the equation describing the Langmuir adsorption isotherm for a gas at a surface.

Define all the quantities involved and their units. Obtain expressions for the dependence of surface coverage on pressure in the limits of low and high pressure.

(7 markah/marks)

TAMAT END