Quantum Numbers — n, l, m, s — allowed values
Atomic Structure
9
JEE Qs
8%
Hard
60
min
Focus on the allowed ranges and interdependencies between n, l, and m_l to swiftly validate or invalidate sets of quantum numbers in problem-solving.
🧮 Key Formulas
✅ Key Points for JEE
- 1Each quantum number describes a specific characteristic of an electron and its orbital: n (energy/size), l (subshell/shape), m_l (orbital orientation), m_s (electron spin).
- 2The allowed values of l are strictly dependent on n (0 to n-1), and m_l on l (-l to +l), forming a hierarchical structure for orbital definition.
- 3A unique set of four quantum numbers (n, l, m_l, m_s) completely and uniquely describes an electron in an atom, according to Pauli's Exclusion Principle.
- 4Be able to quickly identify invalid sets of quantum numbers by checking consistency: l must be less than n, m_l must be between -l and +l (inclusive), and m_s must be +1/2 or -1/2.
- 5Master the calculation of the number of orbitals and maximum electrons for any given shell (n) or subshell (l).
⚠️ Common Mistakes
- ✕Allowing the azimuthal quantum number (l) to be equal to or greater than the principal quantum number (n), e.g., for n=2, l=2 is incorrect.
- ✕Incorrectly determining the range of the magnetic quantum number (m_l), often by forgetting to include 0 or having bounds outside -l to +l.
- ✕Confusing the formulas for the number of orbitals/electrons in a specific subshell (2l+1, 2(2l+1)) with those in a main shell (n^2, 2n^2).
- ✕Assuming the spin quantum number (m_s) can take values other than +1/2 or -1/2, or incorrectly thinking it depends on m_l.
📝 Practice Questions
See allQ57.Given below are two statements : Statement (I) : For a given shell, the total number of allowed orbitals is given by n2 . Statement (II) : For any subshell, the spatial orientation of the orbitals is given by −l to +l values including zero. In the light of the above statements, choose the correct answer from the options given below : (1) Both Statement I and Statement II are false (2) Statement I is true but Statement II is false (3) Both Statement I and Statement II are true (4) Statement I is false but Statement II is true
Q57.In a multielectron atom, which of the following orbitals described by three quantum numbers will have same energy in absence of electric and magnetic fields? A. n = 1, l = 0, m1 = 0 B. n = 2, l = 0, m1 = 0 C. n = 2, l = 1, m1 = 1 D. n = 3, l = 2, m1 = 1 E. n = 3, l = 2, m1 = 0 Choose the correct answer from the options given below: (1) B and C Only (2) A and B Only (3) C and D Only (4) D and E Only
Q51.Radius of the first excited state of Helium ion is given as : a0 → radius of first stationary state of hydrogen atom. (1) r = 4a0 (2) r = 2a0 (3) r = a02 (4) r = a04
Q62.Given below are two statements : Statement (I) : A spectral line will be observed for a 2px →2py transition. Statement (II) : 2Px and 2py are degenerate orbitals. In the light of the above statements, choose the correct answer from the options given below : (1) Both Statement I and Statement II are true (2) Statement I is false but Statement II is true (3) Both Statement I and Statement II are false (4) Statement I is true but Statement II is false
Q51.For hydrogen atom, the orbital/s with lowest energy is/are : (A) 4 s (B) 3px (C) 3 dx2−y2 (D) 3 dz2 (E) 4pz Choose the correct answer from the options given below : (1) (B), (C) and (D) only (2) (A) and (E) only (3) (A) only (4) (B) only
Q44.The frequency of revolution of the electron in Bohr's orbit varies with n, the principal quantum number as (1) 1 (2) 1 n4 n2 (3) 1 (4) 1 n n3
NCERT Chapters
- Class 11 Chemistry Ch 2: Structure of Atom