PEPERIKSAAN IJAZAH SARJANA MUDA SAINS
EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE
SESI AKADEMIK 2016/2017 : SEMESTER II ACADEMIC SESSION 2016/2017 : SEMESTER II
SIC2003 : KIMIA FIZIK II
PHYSICAL CHEMISTRY II
Jun 2017 MASA: 3 jam
June 2017 TIME: 3 hours
ARAHAN KEPADA CALON:
INSTRUCTIONS TO CANDIDATES:
Kertas soalan ini mengandungi Bahagian A, B dan C.
This paper consists of Section A, B and C.
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 10 soalan dalam 12 halaman yang bercetak) (This question paper consists of 10 questions on 12 printed pages)
2/12 BAHAGIAN A (50 MARKAH)
SECTION A (50 MARKS)
Jawab SEMUA soalan dalam seksyen ini.
Answer ALL questions in this section.
1. Soalan-soalan berikut [1(a) – 1(c)] adalah berkenaan asal-usul mekanik kuantum.
The following questions [1(a) – 1(c)] are concerned with the origin of quantum mechanics.
(a) Mengapa radiasi jasad hitam mempunyai spektrum selanjar manakala sinaran daripada atom mempunyai spektrum diskrit?
Why does black body radiation have a continuous spectrum while atomic emissions have discrete spectrum?
(2 markah/ marks) (b) Satu keupayaan berhenti 2.38 volt mencukupi bagi memberhentikan elektron yang dipancarkan daripada potassium dengan cahaya berfrekuensi 1.13 × 1015 s−1. Kira fungsi kerja bagi potassium.
A stopping potential of 2.38 volts just suffices to stop electrons emitted from potassium by the light of frequency of 1.13 × 1015 s−1. Calculate the work function of potassium.
(3 markah/ marks) (c) Mengapa model Bohr mengenai penerangan bagi satu elektron
mengelilingi satu nukles tidak tepat?
Why is the Bohr’s model on the description of an electron circling a nucleus inaccurate?
(2 markah/ marks) 2. Satu elektron bebas dengan fungsi gelombang
A free electron with wave function
𝜓𝑘(𝑥) = 𝐴𝑒𝑖𝑘𝑥
memecut sepanjang paksi 𝑥 kearah 𝑥 = ∞ dari diam melalui satu jatuhan keupayaan 1.000 kV
is accelerated along the 𝑥 axis towards 𝑥 = ∞ from rest through a potential drop of 1.000 kV.
3/12 (a) Kira panjang gelombang akhir de Broglie. Adakah sifat-sifat semacam gelombang jelas kelihatan? Diameter bagi satu atom adalah dalam julat 0.1 ke 0.5 nanometer.
Calculate its final de Broglie wavelength. Would the wavelike properties be very apparent? The diameter of an atom ranges from about 0.1 to 0.5 nanometer.
(4 markah/ marks) (b) Bolehkah fungsi gelombang tersebut dinormalkan? Justifikasi secara
teori jawapan anda.
Can the wave function be normalized? Justify theoretically your answer.
(4 markah/ marks) 3. Satu fungsi eigen bagi satu elektron dalam kotak satu dimensi dengan
panjang 𝐿 diberi oleh
An eigenfunction for an electron in a one-dimensional box of length 𝐿 is given by
𝜓𝑛(𝑥) = (2 𝐿)
1/2
sin (𝑛𝜋𝑥 𝐿 ) Untuk satu elektron dalam keadaan pengujaan kedua, For an electron in the second excited state,
(a) terbitkan nilai eigen dan kira tenaganya.
derive the eigenvalue and calculate the energy.
(4 markah/ marks) (b) kira kebarangkalian bagi menemui elektron tersebut di antara 𝑥 = 0
dan 𝑥 = 0.20𝐿.
calculate the probability for finding the electron between 𝑥 = 0 and 𝑥 = 0.20𝐿.
(4 markah/ marks) (c) dapatkan kebarangkalian bagi menemui elektron tersebut di antara 𝑥 =
0 dan 𝑥 = 0.20𝐿 yang diramalkan oleh fizik klasik.
find probability for finding the electron between 𝑥 = 0 and 𝑥 = 0.20𝐿 predicted by classical physics.
[∫ sin2𝑢 𝑑𝑢 =𝑢 2−1
4sin 2𝑢 + 𝐶]
(1 markah/ marks)
4/12 4. Satu fungsi gelombang bagi pengayun harmonik satu dimensi diberi oleh
A wave function for a one-dimensional harmonic oscillator is given by
𝜓𝑣(𝑥) = 1
(2𝑣𝑣!)1/2(𝛼 𝜋)
1/4
𝑒−𝛼𝑥2/2𝐻𝑣(𝛼1/2𝑥),
dimana where
𝛼 = (𝑘𝑚 ℏ2)
1/2
, 𝑧𝐻𝑛(𝑧) = 𝑛𝐻𝑛−1(𝑧) +1
2𝐻𝑛+1(𝑧), 𝐻0 = 1, 𝐻1 = 2𝑧.
(a) Untuk keadaan dasar, tulis secara lengkap fungsi gelombang bagi pengayun harmonik tiga dimensi (isotropik). Asingkan pembolehubah- pembolehubah. Isotropik bermaksud tidak berubah terhadap arah.
For the ground state, write explicitly the wave function for a three-dimensional (isotropic) harmonic oscillator. Separate variables. Isotropic means invariant with respect to direction.
(3 markah/ marks) (b) Tunjukkan bahawa fungsi gelombang tiga dimensi yang dinyatakan
dalam bahagian 4(a) adalah ortogonal dengan fungsi gelombang tiga dimensi bagi keadaan pengujaan pertama. Guna takrifan fungsi genap dan ganjil dalam menyelesaikan kamiran.
Show that the three-dimensional wave function mentioned in part 4(a) is orthogonal with the three-dimensional wave function of the first excited state.
Use the definition of even and odd functions in solving the integration.
(3 markah/ marks) (c) Dapatkan semua kemungkinan kombinasi nombor-nombor kuantum
untuk paras tenaga bernilai (5
2) ℎ𝜈 bagi pengayun harmonik tiga dimensi (isotropik). Tentukan degenarasinya.
Find all possible combination of the quantum numbers of the energy level having a value of (5
2) ℎ𝜈 for the three-dimensional (isotropic) harmonic oscillator. Determine its degeneracy.
(4 markah/ marks)
5/12 5. Satu fungsi gelombang yang dinormalkan bagi atom semacam hidrogen diberi
oleh
A normalized wave function for the hydrogenlike atom is given by
𝜓(𝑟, 𝜃, 𝜙) = 1 81√6𝜋(𝑍
𝑎0)
7/2
𝑟2𝑒−𝑍𝑟/3𝑎0(3 cos2𝜃 − 1).
Jawab soalan-soalan berikut dalam unit atomik.
Answer the following questions in atomic unit.
(a) Dapatkan nombor kuantum 𝑙 dan 𝑚 bagi keadaan ini.
Find the 𝑙 and 𝑚 quantum numbers for this state.
(2 markah/ marks) (b) Kira magnitud dan komponen z vektor momentum sudut orbital bagi elektron dalam atom tersebut. Lukis diagram-diagram bagi vektor tersebut.
Calculate the magnitude and the z-component of the orbital angular momentum vector for the electron in the atom. Draw the vector diagrams.
(5 markah/marks) (c) Berapa banyak nod jejari yang ada bagi fungsi ini?
How many radial nodes does this function possess?
(1 markah/ marks) (d) Kira tenaga bagi keadaan ini.
Calculate the energy of this state.
(2 markah/ marks) (e) Kira jejari pertukaran klasik bagi keadaan ini.
Calculate the classical turning radius for this state.
(2 markah/ marks)
6/12 6. Pertimbangkan atom litium.
Consider the lithium atom.
(a) Tulis operator Hamiltonian bagi atom tersebut. Jelaskan simbol-simbol yang diguna dalam jawapan anda.
Write the Hamiltonian operator for the atom. Describe the symbols used in your answer.
(2 markah/ marks) (b) Berdasar jawapan anda dalam bahagian 6(a), kenapa persamaan Schrödinger yang berkaitan bagi atom tersebut tidak boleh diselesaikan? Bagaimana anda menyelesaikan masalah ini?
Based on your answer in part 6(a), why is the corresponding Schrödinger equation for the atom unsolvable? How do you resolve this problem?
(2 markah/ marks)
BAHAGIAN B (25 MARKAH) SECTION B (25 MARKS)
Jawab SEMUA soalan dalam seksyen ini.
Answer ALL questions in this section.
7. Dari mekanisma berikut;
From the following mechanism;
(a) Dengan menggunakan pengolahan kaedah keadaan mantap, ungkapkan kadar untuk 𝑑[C2H4I2]
𝑑𝑡 jika kadar permulaan << kadar perambatan.
Using the steady state treatment, deduce the rate expressions for
𝑑[C2H4I2]
𝑑𝑡 if the rate of initiation << rate of the propagation.
(10 markah/ marks)
7/12 (b) Terbitkan ungkapan kadar bagi 𝑑[I2]
𝑑𝑡
,
jika kadar penamatan << kadar perambatan.Deduce the rate expression for 𝑑[I2]
𝑑𝑡 , if the rate of termination << rate of the propagation.
(5 markah/ marks) 8. Kadar tertib pertama bagi tindak balas telah diukur sebagai fungsi suhu,
dimana keputusan berikut diperolehi:
The first order rate constant for the reaction was measured as a function of temperature, with the following results:
Temperature, C k, s-1 27 0.000122.
77 0.228
(a) Tentukan nilai penghalang aktivasi untuk tindak balas ini.
Determine the activation barrier for this reaction.
(5 markah/ marks) (b) Apakah nilai pemalar kadar pada 17 C?
What is the value of the rate constant at 17 C?
(5 markah/ marks)
8/12 BAHAGIAN C (25 MARKAH)
SECTION C (25 MARKS)
Jawab SEMUA soalan dalam seksyen ini.
Answer ALL questions in this section.
9. (a) Untuk sistem tertutup, komposisi sistem tidak dibenarkan untuk berubah. Bagaimana entalpi sistem tertutup berubah dengan tekanan pada suhu malar? Beri jawapan anda dalam sebutan pembolehubah, p, V dan T sahaja.
For a closed system, the composition of the system is not allowed to change.
How does enthalpy of a closed system vary with pressure at constant temperature? Express your answer in terms of variables, p, V and T only.
(4 markah/ marks) (b) Untuk sistem terbuka, komposisi sistem dibenarkan untuk berubah.
Tunjuk hubungan bagi sistem terbuka adalah:
For an open system, the composition of the system is allowed to change.
Show that for an open system:
∑ 𝐻𝑖𝑑𝑛𝑖
𝑘
𝑖=1
= ∑ 𝐺𝑖𝑑𝑛𝑖
𝑘
𝑖=1
(4 markah/ marks) (c) Pada suhu 298.15 K, entalpi molar separa piawai gas metana ialah
𝐻 𝐶𝐻
4(𝑔)
⊖ = −74.81 𝑘𝐽 𝑚𝑜𝑙−1. Hitung keupayaan kimia piawai, 𝜇⊖ gas metana jika entropi mutlak piawai gas metana, karbon dan gas hidrogen pada suhu yang sama mempunyai nilai seperti berikut:
At 298.15 K, the standard partial molar enthalpy of methane gas is 𝐻 𝐶𝐻
4(𝑔)
⊖ =
−74.81 𝑘𝐽 𝑚𝑜𝑙−1. Calculate the standard chemical potential, 𝜇⊖ for methane gas when the standard absolute entropies of methane gas, carbon and hydrogen gas at the same temperature are reported to be:
𝑆𝐶𝐻
4(𝑔)
⊖ = 186.26 𝐽 𝑚𝑜𝑙−1𝐾−1 𝑆𝐶(𝑠)⊖ = 5.740 𝐽 𝑚𝑜𝑙−1𝐾−1 𝑆𝐻
2(𝑔)
⊖ = 130.684 𝐽 𝑚𝑜𝑙−1𝐾−1
(5 markah/ marks)
9/12 10. (a) Terbit persamaan Gibbs-Helmholtz dan seterusnya tunjuk bagaimana
ungkapan 𝜕
𝜕𝑇(ln 𝐾𝑝) =∆𝐻⊝
𝑅𝑇2 diperolehi. Apakah kepentingan persamaan Gibbs-Helmholtz?
Derive the Gibbs-Helmholtz equation and subsequently show how the expression 𝜕
𝜕𝑇(𝑙𝑛 𝐾𝑝) =∆𝐻⊝
𝑅𝑇2 is obtained. What is the importance of the Gibbs- Helmholtz equation?
(7 markah/ marks) (b) Lakar pergantungan tenaga bebas Gibbs kepada suhu untuk gas, cecair dan pepejal bagi suatu bahan tulen. Jelas bagaimana pertambahan dalam tekanan memberi kesan ke atas titik lebur bahan di mana 𝑉̅𝑐𝑒𝑐𝑎𝑖𝑟 > 𝑉̅𝑝𝑒𝑝𝑒𝑗𝑎𝑙 . Beri lakaran gambarajah yang sesuai.
Sketch the dependence of Gibbs free energy on temperature for the gas, liquid and solid phases of a pure substance. Explain how does an increase in pressure affect the melting point of the substance whereby 𝑉̅𝑙𝑖𝑞𝑢𝑖𝑑 > 𝑉̅𝑠𝑜𝑙𝑖𝑑 Include appropriate graphical sketch.
(5 markah/ marks)
10/12 Lampiran
Appendix
Beberapa Nilai Pemalar dan Faktor Penukaran yang Berguna Values of Some Useful Constants and Conversion Factors
11/12
12/12 TAMAT
END
