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4. (20 points). Consider a deuterium atom (composed of a nucleus with spin I - 1...
Problem 1. (20 points) Consider two electrons, each with spin angular momentum s,-1/2 and orbital angular momentum ,-1....
Problem 1. (20 points) Consider two electrons, each with spin angular momentum s,-1/2 and orbital angular momentum ,-1. (a) (3 points) What are the possible values of the quantum number L for the total orbital angular momentum L-L+L,? (b) ( 2 points) What are the possible values of the quantum number S for the total spin angular momentum S-S,+S, (c) Points) Using the results from (a) and (b), find the possible quantum number J for the total angular momentum J-L+S....
3. Knowing that the magnesium and aluminum atoms possesses 12 and 13 electrons respectively: (a) Write...
3. Knowing that the magnesium and aluminum atoms possesses 12 and 13 electrons respectively: (a) Write down the electron configuration (nl) of the ground state. Explain your answer. (b) We focus on the electron configuration determined in (a). Considering only the electrons from the outer subshell, add their electronic spins and their orbital angular momenta separately. Label the total spin and the total orbital momentum quantum numbers by s and l, respectively. Write down the possible values spanned by s...
3. Knowing that the magnesium and aluminum atoms possesses 12 and 13 electrons respectively: (a) Write...
3. Knowing that the magnesium and aluminum atoms possesses 12 and 13 electrons respectively: (a) Write down the electron configuration (nl) of the ground state. Explain your answer. (b) We focus on the electron configuration determined in (a). Considering only the electrons from the outer subshell, add their electronic spins and their orbital angular momenta separately. Label the total spin and the total orbital momentum quantum numbers by s and l, respectively. Write down the possible values spanned by s...
PLEASE COMPLETE B) and stay tuned for my following 2 questions where I will ask part c) and d). P...
PLEASE COMPLETE B) and stay tuned for my
following 2 questions where I will ask part c) and d). Part a) has
already been posted.
The lowest energy state of a hydrogen-like atom has total angular momentum J-1/2 (from the l-O orbital angular momentum and the electron spin s 1/2). Furthermore, the nucleus also has a spin, conventionally labeled I (for hydrogen, this is the proton spin, 1 1/2). This spin leads to an additional degeneracy. For example, in the...
Consider the hydrogen atom and its eigenstates, omitting any effects of fine structure (spin- orb...
Consider the hydrogen atom and its eigenstates, omitting any effects of fine structure (spin- orbit coupling). For the state y21-1 give the a. expectation value of the energy b. c. expectation value of the z-component of the orbital angular momentum d. expectation value of the y-component of the orbital angular momentum e. Now replace the electron with a muon which has a mass mu200 me. What is the ratio expectation value of the total orbital angular momentum of the ground...
1: Part A: Two electrons occupy the 2s shell in a Be atom (Z = 4)....
1: Part A: Two electrons occupy the 2s shell in a Be atom (Z = 4). What are the possible quantum numbers J for the total angular momentum of this two-electron system, neglecting any contributions from the nucleus or 1s level? Part B: Calculate the energy required to cause an electron from the 2s shell to jump to each of the 2p, 3s, 3p, and 3d states. E1 for Be is 9.3 eV. En = (-Z2E1)/n2. One of the listed...
An electron in an atom is in the n=2 state, where n is the principle quantum...
An electron in an atom is in the n=2 state, where n is the principle quantum number. What possible values could the orbital quantum number take? What possible values could the magnetic orbital quantum number take? What are the possible values of the Orbital Angular Momentum (L)? What are the possible values of ???
Which of the following set of quantum numbers (ordered n,l,ml,ms) are possible for an electron in...
Which of the following set of quantum numbers (ordered
n,l,ml,ms) are possible for an electron in an atom?
Quantum Number Rules Learning Goal: To learn the restrictions on each quantum number. Quantum numbers can be thought of as labels for an electron. Every electron in an atom has a unique set of four quantum numbers. The principal quantum number n corresponds to the shell in which the electron is located. Thus n can therefore be any integer. For example, an...
Tl 6. (4 pts) We calculated Ahf for the ground state Hydrogen atom, but now let us consider Hht f...
Tl 6. (4 pts) We calculated Ahf for the ground state Hydrogen atom, but now let us consider Hht for the ground state of the deuterium atom. The basic idea is the same: Here the matrix representation of S is the same, since it represents the spin operator for the spin- electron, but that of 7 is different because the deuteron is a spin-1 particle (neutron+proton) whose spin has 3 possible values for the magnetic quantum number. Also, we must...
Part D and E A spin-orbit interaction between a spin and an orbital motion has the...
Part D and E
A spin-orbit interaction between a spin and an orbital motion has the form HS-o = Bs. (1) Assume that S= } for the spin and 1 = 1 for the orbital angular momentum. A. Write down the basis states without the spin-orbit interaction in terms of a direct product of spin eigenstates and orbital angular momentum eigenstates, such as 1,1 > > B. Using angular momentum summation rules, write down all possible values of j and...
Problem 1. (20 points) Consider two electrons, each with spin angular momentum s,-1/2 and orbital angular momentum ,-1. (a) (3 points) What are the possible values of the quantum number L for the total orbital angular momentum L-L+L,? (b) ( 2 points) What are the possible values of the quantum number S for the total spin angular momentum S-S,+S, (c) Points) Using the results from (a) and (b), find the possible quantum number J for the total angular momentum J-L+S....
PLEASE COMPLETE B) and stay tuned for my
following 2 questions where I will ask part c) and d). Part a) has
already been posted.
The lowest energy state of a hydrogen-like atom has total angular momentum J-1/2 (from the l-O orbital angular momentum and the electron spin s 1/2). Furthermore, the nucleus also has a spin, conventionally labeled I (for hydrogen, this is the proton spin, 1 1/2). This spin leads to an additional degeneracy. For example, in the...
Consider the hydrogen atom and its eigenstates, omitting any effects of fine structure (spin- orbit coupling). For the state y21-1 give the a. expectation value of the energy b. c. expectation value of the z-component of the orbital angular momentum d. expectation value of the y-component of the orbital angular momentum e. Now replace the electron with a muon which has a mass mu200 me. What is the ratio expectation value of the total orbital angular momentum of the ground...
Which of the following set of quantum numbers (ordered
n,l,ml,ms) are possible for an electron in an atom?
Quantum Number Rules Learning Goal: To learn the restrictions on each quantum number. Quantum numbers can be thought of as labels for an electron. Every electron in an atom has a unique set of four quantum numbers. The principal quantum number n corresponds to the shell in which the electron is located. Thus n can therefore be any integer. For example, an...
Tl 6. (4 pts) We calculated Ahf for the ground state Hydrogen atom, but now let us consider Hht for the ground state of the deuterium atom. The basic idea is the same: Here the matrix representation of S is the same, since it represents the spin operator for the spin- electron, but that of 7 is different because the deuteron is a spin-1 particle (neutron+proton) whose spin has 3 possible values for the magnetic quantum number. Also, we must...
Part D and E
A spin-orbit interaction between a spin and an orbital motion has the form HS-o = Bs. (1) Assume that S= } for the spin and 1 = 1 for the orbital angular momentum. A. Write down the basis states without the spin-orbit interaction in terms of a direct product of spin eigenstates and orbital angular momentum eigenstates, such as 1,1 > > B. Using angular momentum summation rules, write down all possible values of j and...
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