# Quantum numbers problems and solutions

1. What is the principal quantum number (n) for an electron in the 3s subshell? Solution: The principal quantum number for the 3s subshell is 3.

2. How many orbitals are present in a 4f subshell? Solution: The 4f subshell has 7 orbitals.
3. What are the possible values of the magnetic quantum number (ml) for an electron in a 4f orbital? Solution: The possible values of ml for a 4f orbital are -3, -2, -1, 0, 1, 2, 3.
4. Which quantum number indicates the shape of an orbital? Solution: The azimuthal quantum number (l) indicates the shape of an orbital.
5. What is the azimuthal quantum number (l) for an electron in the 2p subshell? Solution: The azimuthal quantum number for a 2p subshell is 1.
6. How many total orbitals are there in the third energy level (n=3)? Solution: The total number of orbitals in the third energy level is given by n², so there are 3² = 9 orbitals.
7. What does the spin quantum number (ms) of -½ signify? Solution: The spin quantum number of -½ signifies that the electron is spinning in the opposite direction to the one spinning with a +½ spin quantum number.
8. How many electrons can occupy the 3d subshell? Solution: The 3d subshell can hold a maximum of 2×5 = 10 electrons.
9. What is the magnetic quantum number (ml) for an electron in the s orbital? Solution: The magnetic quantum number for an electron in the s orbital is 0.
10. How many electrons are in the 2s subshell of a lithium (Li) atom? Solution: The electron configuration of lithium is 1s² 2s¹, so there is 1 electron in the 2s subshell.
11. Which quantum number is associated with the orientation of an orbital in space? Solution: The magnetic quantum number (ml) is associated with the orientation of an orbital in space.
12. How many orbitals are there in a p subshell? Solution: A p subshell has 3 orbitals.
13. How many total electrons can be found in the second energy level (n=2)? Solution: The total number of electrons that can be found in the second energy level is given by 2n², so there are 2×2² = 8 electrons.
14. What is the spin quantum number (ms) for an electron in a magnesium (Mg) atom? Solution: The spin quantum number for any electron can only be either +½ or -½.
15. How many electrons are in the 2p subshell of a nitrogen (N) atom? Solution: The electron configuration of nitrogen is 1s² 2s² 2p³, so there are 3 electrons in the 2p subshell.
16. What is the principal quantum number (n) for an electron in the outermost shell of an oxygen (O) atom? Solution: Oxygen is in the 2nd period of the periodic table, so the principal quantum number for its outermost shell is 2.
17. Which quantum number determines the energy of an electron in a hydrogen atom? Solution: The principal quantum number (n) determines the energy of an electron in a hydrogen atom.
18. How many electrons can be held in the n=4 energy level? Solution: The n=4 energy level can hold a maximum of 2n² = 2×4² = 32 electrons.
19. What are the four quantum numbers (n, l, ml, ms) for the last electron added to a phosphorus (P) atom? Solution: The electron configuration of phosphorus is [Ne] 3s² 3p³. The four quantum numbers for the last electron added are n=3, l=1, ml=1, ms=+½.
20. What does the azimuthal quantum number (l) of 3 represent? Solution: The azimuthal quantum number of 3 represents an f subshell.