Quantum Numbers n l m s - UNSOLVED PRACTICE SET
Chapter: Structure of Atom | Topic: Quantum Numbers n l m s
QUANTUM NUMBERS N L M S - UNSOLVED PRACTICE SET
Topic: Quantum Numbers n l m s
Multiple Choice Questions
Q1. The principal quantum number (n) determines:
- The shape of the orbital
- The size and energy of the orbital
- The orientation of the orbital
- The spin of the electron
Q2. The azimuthal quantum number (l) can have values from:
- 0 to n
- 0 to (n − 1)
- 1 to n
- −l to +l
Q3. The magnetic quantum number (m_l) for l = 2 can have values:
- −2, −1, 0, +1, +2
- −3, −2, −1, 0, +1, +2, +3
- 0, +1, +2
- −1, 0, +1
Q4. The spin quantum number (m_s) can have values:
- +1/2 and −1/2
- +1 and −1
- 0 and +1
- Any value between −1 and +1
Q5. For n = 3, the possible values of l are:
- 0, 1
- 0, 1, 2
- 1, 2, 3
- 0, 1, 2, 3
Q6. The total number of orbitals in a shell with principal quantum number n is:
- n
- n²
- 2n²
- n³
Short Answer Questions
Q7. Name the four quantum numbers and state what each one describes.
Q8. What are the possible values of l for n = 4? Name the subshells corresponding to each value of l.
Q9. How many orbitals are present in the n = 3 shell? List them with their quantum numbers.
Q10. What is the significance of the spin quantum number? Why must two electrons in the same orbital have opposite spins?
Q11. Your school library has a unique book-finding system: the first number tells you the floor (1 to 4), the second tells you the section (A, B, C), the third tells you the shelf (1 to 5), and a colour code tells you if the book is hardcover or paperback. How is this exactly analogous to the four quantum numbers that describe an electron's location in an atom?
Q12. An electron has quantum numbers n = 3, l = 2, m_l = −1, m_s = +1/2. Identify the orbital in which this electron is present.
Long Answer Questions
Q13. Explain the four quantum numbers in detail. For each quantum number, discuss:
(a) Its symbol and name
(b) The information it provides
(c) Its possible values
(d) Its relationship to other quantum numbers
Illustrate with the example of an electron with n = 4, l = 2, m_l = 0, m_s = −1/2.
Q14. Describe how quantum numbers arise from the quantum mechanical model. Explain the physical significance of each quantum number and how they restrict the number of electrons in an atom. Show that the maximum number of electrons in a shell is 2n² and in a subshell is 2(2l + 1).
Q15. A teacher gives you the following challenge: "Without looking at the periodic table, determine how many electrons can have the following sets of quantum numbers."
(a) n = 2
(b) n = 3, l = 1
(c) n = 4, l = 2, m_l = 0
(d) n = 3, l = 2, m_l = +1, m_s = +1/2
For each case, explain your reasoning step by step. Also, explain why the set n = 2, l = 2, m_l = 0 is not allowed.
Numerical / Application-Based Problems
Q16. For an electron in an atom:
(a) List all possible sets of quantum numbers for the 3p subshell.
(b) How many electrons can occupy the 3d subshell? List all possible combinations of m_l and m_s for one of the 3d orbitals.
(c) An electron has n = 4 and l = 3. How many other electrons can share the same subshell? What is the name of this subshell?
Q17. Consider the following sets of quantum numbers. Identify which are allowed and which are not allowed. For those not allowed, state the reason.
| Set | n | 1 | m_l | m_s |
|---|---|---|---|---|
| A | 3 | 2 | -2 | +1/2 |
| B | 2 | 2 | 0 | −1/2 |
| C | 4 | 0 | 0 | +1/2 |
| D | 3 | 1 | +2 | +1/2 |
| E | 2 | 1 | -1 | 0 |
Q18. A hydrogen atom in its ground state has one electron with quantum numbers n = 1, l = 0, m_l = 0, m_s = +1/2.
(a) If this electron is excited to n = 5, how many different sets of quantum numbers are possible for the excited electron?
(b) How many of these correspond to the 5d subshell?
(c) If two electrons are placed in the 1s orbital, what must be their spin quantum numbers? What principle governs this?
(d) Calculate the total number of electrons that can have n = 3 in an atom. Show your calculation using quantum number rules.