Reading Quiz

Question 1:

In the (fully) quantum theory of the hydrogen atom, there are four quantum numbers for the electron. What are these four quantum numbers, what values can they take on, and what is the PHYSICAL QUANTITY they are associated with?

Answer:

  1. The electron's energy, n. n is a positive integer; the magnitude of the electron's orbital angular momentum, l. l=0,1,2,...,n-1; the z component of the orbital angular momentu, ml. ml=-l, -l+1, ...,l+1, l; and the z component of the spin angular momentum, ms. ms= +/- 1/2.
  2. n - distance-dependence of wavefunction l - orbital angular momentum m - component of angular momentum
  3. The four numbers are n, L, m(l), and m(s). n, L, and m(l) are associated with a a spherical coordinate for location in space. n is the energy (the principal quantum number) and can be any positive, non-zero integer. L (the orbital quantum number) is the magnitude of the electron's angular momentum and can be any positice integer between 0 and n-1. m(l) (the magnetic quantum number) is the z-component of the the electron's orbital angular momentum and can be any integer between -L and L. m(s) is the spin quantum number and can be any half integer value.
  4. Respectively: n, l, ml, ms; positive integer, integers from 0 to n-1, integers from -l to +l, +/-.5; energy level, orbital angular momentum, z-component of orbital angular momentum, z-component of spin.
  5. n is the energy level of the electron and can only be a. l is related to the magnitude of the orbital angular momentum of the electron and is 0 for the Hydrogen atom. m subscript l related to the z component of the orbital angular momentum and is 0. m subsript s is the spin of the electron and can be either 1/2 or -1/2.
  6. Principal - 1,2,3,... related to the probability of finding the particle at certain distances from the nucleus Orbital- 0,1,2,... , n-1 relates to the angular dependence of the electic wave function magnetic- -l, -(l-1),....,l-1, l related to the angular momentum as the particle moves through space.
  7. Spin (angular momentum), Principal quantum number (dependency of the wave function on r), orbital quantum number (anular momentum), and magnetic quantum number (angular momentum along some direction in space).
  8. The four quantum numbers are n, l, ml, ms. They are associated with the electron's energy, the magnitude of the electron's orbital angular momentum, the z-component of its orbital angular momentum, and the z-component of the spin angular momentum respectively.
  9. The four quantum numbers are n, l, m. n is associated with the probability of finding the electron a distance r from the nucleous and can be 1, 2, 3, ... . l is associated with the angular momentum and can be 0 ,1 ,2, ... n-1. ml has to do with when the electrom is in a magnetic field and can be any integer from -l to l. And ms has to do with the spin and for the eletron this can be -1/2 or 1/2
  10. N is the principal quantum number and tells you what enegy level you are in. L is the orbital quantum number and tells you the angular momentum, while m is the magnetic quantum number and tells you what its angular momentum is relative to a certain direction. m can be -1,0,1, l can be 1,-1
  11. n=1,which represents the electrons energy, l=0,which represents the electrons w m(l)=0, which is the z component of w,m(s) is the spin component of the angular frequency

Question 2:

Compare and contrast what the Bohr Model and the Quantum Mechanical Model of the hydrogen say (if anything) about the energy of the electron.

Answer:

  1. They say the same things about energy of the electron
  2. They both say there are discrete energy levels, and specify what they are the same way
  3. The Bohr model of hydrogen says that the eneregy of the electron has to be quantized since it can only be in certain states so that it does not radiate away it's energy The equations also use a Z value that can only be integer values. The Quantum Mechanical Model also says the energy has to be quantized because the priciple quantum number can only be integer values.
  4. They are the same.
  5. They both have quantized energy states, but the Quantum Model has substates between the energy levels n to explain the number of electrons that fit in an energy level.
  6. They each have different values as a result that the bohr model is based on classical electromagnetic theory and the quantum theory is obviously not., but both are bound to the scrodinger equation.
  7. The engergies are the same for the two models.
  8. The energies are the same as in the Bohr model.
  9. For the energy of the electrom both models agree on the values.
  10. Quantum mechanical model talks about probability density and where the electron could be, while Bohr model just says where the electron is, not taking probability into account.
  11. in the case of the H atom the energy given by both is the same

Question 3:

Compare and contrast what the Bohr Model and the Quantum Mechanical Model of the hydrogen say (if anything) about the orbital angular momentum of the electron.

Answer:

  1. The quantum model says that teh magnitude of orbital angular momentm is equal to the square root of l times l+1 times hbar
  2. for hydrogen - the same: it's hbar
  3. Bohr said that angular momentum must be quantized as an integer multiple of h-bar. Since the orbital quantum number can only be integer values, it is quantized as well in the QM model.
  4. In the quantum mechanical model r=a/Z, in the Bohr model it's r=a.
  5. The Bohr model had angular momentum that was from the electron orbiting the atom at a specific speed and was quantized. mvr=n*h bar. The Quantum Model has the orbital angular momentum described by the quantum number for l. The momentum is then found by L=Sqrt(l(l+1))*h bar.
  6. The Bohr Model and the Quantum Model, boith say that the angular momentum is quantized. But they have different values for it.
  7. it is related to the square root of l
  8. The quantum mechanical model tells us that the energy does not depend on l. It only depends on l when the atom has several electrons.
  9. For angular momentum, in the ground state, for the quantum model the momentum is 0, however for the Bohr model the momentum is h bar.
  10. Quantum mechanics dels with orbital angular momentum in much the same as the Bohr model, they both have it and it is a real quantity.
  11. the quantum theory provides us with the angular momentum of the electrons in H but in this case the value is 0 so both modles work

Question 4:

Compare and contrast what the Bohr Model and the Quantum Mechanical Model of the hydrogen say (if anything) about the z-component of the orbital angular momentum of the electron.

Answer:

  1. the quantum model says that the z component of angular momentum =ml times hbar
  2. Bohr: nothing Quantum: 0
  3. For an electron, Bohr doesn't say anything about the z-component of orbital angular momentum. QM says that this is also quantized by half values since it is a fermion.
  4. The Bohr model doesn't include ml.
  5. The Quantum Model has angular momentum in the z direction equal to m subscript l times h bar.
  6. the bohr model doesn't say anything about the z-component specifically, but it givea simular value to quanum models angular momentum in the z direction.
  7. it is given by m sub l times h-bar
  8. The only time the energy depends on ml is when it is in a magnetic field.
  9. Spin is the same.
  10. The equation still holds, but in quantum mechanics to account for intrinsic spin you get double the vslue that you would expect.
  11. once again the bohr modle basicaly works for the H atom b/c of its simplisity

Question 5:

What concept(s) or application(s) from the reading did you find interesting or intriguing? Anything you'd like to discuss further?

Answer:

  1. not really
  2. It's interesting how Bohr's model works so well until you get to helium
  3. I like the periodic table explanation in terms of physics (even though I didn't quite get all of it) because I'm not a chemistry fan.
  4. N/A
  5. The explainations for the energy levels the sublevels and the number of electrons that can fit in each using quantum mechanics. It makes more sence now that there is a reason for it.
  7. I'm just really confused...
  8. Nope
  9. The periodic table makes a lot of sense from a quantum perpective.
  10. I would like to learn more about the quantum mechanical model, because it is very strange.

Question 6:

What (if any) were the conceptual or mathematical difficulties that you had with this reading? What do we need to spend class time on?

Answer:

  1. none
  3. I remember something about the four quantum numbers from chemistry now that i read about them but i don't think we ever really did anything with them. The book goes right from spherical coordinates to the quantum numbers but the supplementary book doesn't mention spherical coordinates. what is the realtionship? is n the radius of the orbit or the energy of the electron or both?
  4. N/A
  5. The math for the radial Schrodinger equations was confusing.
  6. could you go over what z actually is again? especailly what z is to an observer and what it is to x and y.
  7. Ugliness of spherical coordinates? I'm pretty bad at those :-/
  8. A lot of it was fairly new. A discussion about it all in class would probably help.
  9. Nope.
  10. I had difficulty with why the quantum mechanical model is so much better than Bohr's model, is there going to come along a method even weirder than quantum mechanics that is better thn that?