4. Answer the following: a. For n = 4, what is the largest allowed value of (? b. What is the magnitude of the corresponding orbital angular momentum for { =3? c. Draw the possible orientations of the orbital angular momentum vector L for { =3. d. How many different projections on the z-axis may this angular momentum vector have? e. What is the magnitude of the largest projected component? f. What is the smallest angle that the angular momentum vector can make with the z- axis?
4. Answer the following: a. For n = 4, what is the largest allowed value of (? b. What is the magnitude of the corresponding orbital angular momentum for { =3? c. Draw the possible orientations of the orbital angular momentum vector L for { =3. d. How many different projections on the z-axis may this angular momentum vector have? e. What is the magnitude of the largest projected component? f. What is the smallest angle that the angular momentum vector can make with the z- axis?
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![Sheet (9) – Introduction to Magnetism
1. What is the angular momentum of a particle of mass m, moving in a circle of radius r with an
angular velocity o?
2. From the rules governing the use of quantum numbers, show that the K, L and M shells in an atom
can accommodate at most 2, 8, and 18 electrons, respectively.
3. For each of the following atoms and ions, sketch the electronic structure, using a box for orbital
wave functions and arrow (up or down) for an electron:
a. Manganese, [Ar] 3d°4s²
b. Cobalt, [Ar] 3d²4s?
4. Answer the following:
a. For n = 4, what is the largest allowed value of €?
b. What is the magnitude of the corresponding orbital angular momentum for { =3?
c. Draw the possible orientations of the orbital angular momentum vector L for { =3.
d. How many different projections on the z-axis may this angular momentum vector
have?
e. What is the magnitude of the largest projected component?
f. What is the smallest angle that the angular momentum vector can make with the z-
axis?
5. Show the possible orientations of the orbital angular momentum vector L for { = 0, 1, 2, 3, and 4.
Physical Constants:
h= 6.63 × 10-34 J/sec](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c0a9129-3cd9-493f-ba3c-58fc6e560311%2F4a226b46-34ab-4ab6-97ed-f5f3573d3c41%2Foz2xed_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Sheet (9) – Introduction to Magnetism
1. What is the angular momentum of a particle of mass m, moving in a circle of radius r with an
angular velocity o?
2. From the rules governing the use of quantum numbers, show that the K, L and M shells in an atom
can accommodate at most 2, 8, and 18 electrons, respectively.
3. For each of the following atoms and ions, sketch the electronic structure, using a box for orbital
wave functions and arrow (up or down) for an electron:
a. Manganese, [Ar] 3d°4s²
b. Cobalt, [Ar] 3d²4s?
4. Answer the following:
a. For n = 4, what is the largest allowed value of €?
b. What is the magnitude of the corresponding orbital angular momentum for { =3?
c. Draw the possible orientations of the orbital angular momentum vector L for { =3.
d. How many different projections on the z-axis may this angular momentum vector
have?
e. What is the magnitude of the largest projected component?
f. What is the smallest angle that the angular momentum vector can make with the z-
axis?
5. Show the possible orientations of the orbital angular momentum vector L for { = 0, 1, 2, 3, and 4.
Physical Constants:
h= 6.63 × 10-34 J/sec
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