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1. (a) (10 pt) Which of the following wavefunctions CAN be a valid total wavefunction for...
1. An excited state electron configuration of He is given by 2p'3d (a) Determine all the possible...
1. An excited state electron configuration of He is given by 2p'3d (a) Determine all the possible term symbols of this electron configurations. b) Now consider the following box notation (one way to arrange 2p 3d1). p-orbital d-orbital m,-+1 0 .1 m,: +2 +1 0-1 -2 (b-1) Write all the possible (valid) wavefunctions that match with the electron configuration in the above box notation. No need to determine the normalization constant. (b-2) Find all the possible term symbols in (a)...
Two-electron system. (A) Which of the following are physically valid wavefunctions for a two-electron system such as th...
Two-electron system. (A) Which of the following are physically valid wavefunctions for a two-electron system such as the He atom or the H2 molecule? (B) What property makes them physically valic wavefunctions? (a) y(12)-1s(1)a(1) . 1s(2)A(2) (c) Ψ(1,2)-Isa(1)IsE(2)-1sa(2)1sE(1). Multi-electron atom. Consider a sodium cation, Nat. (A) How many variables does the multi-electron wavefunction describing its ground state depend on? (B) How many kinetic-energy, repulsion and attraction terms are in the associated Hamiltonian?
Two-electron system. (A) Which of the following are...
1. Given the following wavefunction for the ground state of a finite quantum well of width 2nm, g...
1. Given the following wavefunction for the ground state of a finite quantum well of width 2nm, ground state energy of E1=0.05eV -A cos(kx) and ψ,-Beax A.) Find the values of k and a (remember to keep the wavefunction continuous and smooth)[10ptsl B.) Find the normalization constants A and B (you will need to find k first of course) [10pts] C.) Determine the barrier energy from the decay constant a? [5pts D.)If the well were replaced with a semi-infinite well...
Q 1: For particle in a box problem, answer the following questions, a) Why n=0 is...
Q 1: For particle in a box problem, answer the following questions, a) Why n=0 is not an allowed quantum number? b) En = 0 is not allowed for particle in a box, why? c) Ground state wavefunction is orthogonal to the first excited state wavefunction, what does it mean? Q 2: An electronic system that is treated as particle in 3-D box with dimensions of 3Å x 3Å x 4Å. Calculate the wavelength corresponding to the lowest energy transition...
QUESTION 3: Atomic Structure 2 [25 total marks] (a) (1) What is the photoelectric effect? (2...
QUESTION 3: Atomic Structure 2 [25 total marks] (a) (1) What is the photoelectric effect? (2 marks) (ii) Find the frequency of incident photon on the surface of a metal if the threshold wavelength is 500 nm and the velocity of electron is 6 x 10 ms. (8 marks) (b) Considering the equation for the energy levels of a hydrogenic atom below, calculate the frequency of the transition between the ground and first excited electronic states of the hydrogen atom,...
1 From Wavefunction to Bra-Ket In bra-ket notation, a state y(x) is written as a ket:...
1 From Wavefunction to Bra-Ket In bra-ket notation, a state y(x) is written as a ket: 14) + (2). The inner product between two states 41(2), 42(2) is written as a bra-ket: (441\42) = |dx (z)* #2(a). If a state is a complex linear combination |V) = a1 (41) + a2 (42), then its corresponding bra is (V= a1 (01| +a(42 In this problem, we will use the simple harmonic oscillator as a concrete example. The energy eigenstates of the...
5. A particle in the harmonic oscillator potential has the initial wave function Psi(x, 0) = A[\psi_{0}(x) + \psi_{1}(x)] for some constant A. Here to and ₁ are the normalized ground state and the first excited state wavefunctions of the harmonic oscill
5. A particle in the harmonic oscillator potential has the initial wave function Psi(x, 0) = A[\psi_{0}(x) + \psi_{1}(x)] for some constant A. Here to and ₁ are the normalized ground state and the first excited state wavefunctions of the harmonic oscillator, respectively. (a) Normalize (r, 0). (b) Find the wavefunction (r, t) at a later time t and hence evaluate (x, t) 2. Leave your answers involving expressions in to and ₁. c) sing the following normalized expression of...
eleven an energy level? eren 15) Why does it take more energy to remove an electron...
eleven an energy level? eren 15) Why does it take more energy to remove an electron from Althan from Al? 16) Distinguish between an atom in its ground state and an excited atom. 17) Which of the following notations shows the electron configuration of a neutral atom in an excited state? Name the element, and explain how you know if it is excited or not: 1s 2s 2p' (b) 1s 2s 2p 3s! Oxygen is in excited States oxygen crtom...
Physical Chemistry 8. The following questions pertain to the ground (1s) and first two excited (2s...
Physical Chemistry
8. The following questions pertain to the ground (1s) and first two excited (2s and 2p) states of (a) What is the expectation value of the radius (b) What is the expectation value of the poten- (c) What is the expectation value of the kinetic (d) Which of the above states has the largest (e) What is the term symbol of a Li?+ ion in a (f) If the Stern-Gerlach experiment were per- a lithium cation (Li2+). in...
question 7 9 10 ), where n, a, and are constant, is an eigenfunction of p....
question 7 9 10
), where n, a, and are constant, is an eigenfunction of p. 7. (a) p. =- what is p. ? (b) sin( i ax what is the eigenvalue? (107) (9) = v ydt for a normalized wavefunction. Please find (1) for(a) v. - and (b) 42p. 4/2008 re s in sind. (hint : integrate over all space: sin Odrdodø (sin? xdx = [l-c952de, 5 xede = (203) 3 2 10. A particle of mass m is...
1. An excited state electron configuration of He is given by 2p'3d (a) Determine all the possible term symbols of this electron configurations. b) Now consider the following box notation (one way to arrange 2p 3d1). p-orbital d-orbital m,-+1 0 .1 m,: +2 +1 0-1 -2 (b-1) Write all the possible (valid) wavefunctions that match with the electron configuration in the above box notation. No need to determine the normalization constant. (b-2) Find all the possible term symbols in (a)...
Two-electron system. (A) Which of the following are physically valid wavefunctions for a two-electron system such as the He atom or the H2 molecule? (B) What property makes them physically valic wavefunctions? (a) y(12)-1s(1)a(1) . 1s(2)A(2) (c) Ψ(1,2)-Isa(1)IsE(2)-1sa(2)1sE(1). Multi-electron atom. Consider a sodium cation, Nat. (A) How many variables does the multi-electron wavefunction describing its ground state depend on? (B) How many kinetic-energy, repulsion and attraction terms are in the associated Hamiltonian?
Two-electron system. (A) Which of the following are...
1. Given the following wavefunction for the ground state of a finite quantum well of width 2nm, ground state energy of E1=0.05eV -A cos(kx) and ψ,-Beax A.) Find the values of k and a (remember to keep the wavefunction continuous and smooth)[10ptsl B.) Find the normalization constants A and B (you will need to find k first of course) [10pts] C.) Determine the barrier energy from the decay constant a? [5pts D.)If the well were replaced with a semi-infinite well...
QUESTION 3: Atomic Structure 2 [25 total marks] (a) (1) What is the photoelectric effect? (2 marks) (ii) Find the frequency of incident photon on the surface of a metal if the threshold wavelength is 500 nm and the velocity of electron is 6 x 10 ms. (8 marks) (b) Considering the equation for the energy levels of a hydrogenic atom below, calculate the frequency of the transition between the ground and first excited electronic states of the hydrogen atom,...
1 From Wavefunction to Bra-Ket In bra-ket notation, a state y(x) is written as a ket: 14) + (2). The inner product between two states 41(2), 42(2) is written as a bra-ket: (441\42) = |dx (z)* #2(a). If a state is a complex linear combination |V) = a1 (41) + a2 (42), then its corresponding bra is (V= a1 (01| +a(42 In this problem, we will use the simple harmonic oscillator as a concrete example. The energy eigenstates of the...
eleven an energy level? eren 15) Why does it take more energy to remove an electron from Althan from Al? 16) Distinguish between an atom in its ground state and an excited atom. 17) Which of the following notations shows the electron configuration of a neutral atom in an excited state? Name the element, and explain how you know if it is excited or not: 1s 2s 2p' (b) 1s 2s 2p 3s! Oxygen is in excited States oxygen crtom...
Physical Chemistry
8. The following questions pertain to the ground (1s) and first two excited (2s and 2p) states of (a) What is the expectation value of the radius (b) What is the expectation value of the poten- (c) What is the expectation value of the kinetic (d) Which of the above states has the largest (e) What is the term symbol of a Li?+ ion in a (f) If the Stern-Gerlach experiment were per- a lithium cation (Li2+). in...
question 7 9 10
), where n, a, and are constant, is an eigenfunction of p. 7. (a) p. =- what is p. ? (b) sin( i ax what is the eigenvalue? (107) (9) = v ydt for a normalized wavefunction. Please find (1) for(a) v. - and (b) 42p. 4/2008 re s in sind. (hint : integrate over all space: sin Odrdodø (sin? xdx = [l-c952de, 5 xede = (203) 3 2 10. A particle of mass m is...
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