Question

Which of the following statements is not true for an electron with quantum numbers n = 4 and m = 2?
1. The electrons may have the quantum number s = +1/2
2. The electrons may have the quantum number l = 2
3. The electrons may have the quantum number l = 3
4. The electrons may have the quantum number l = 4

Answer 1

Correct Answer - Option 4 : The electrons may have the quantum number l = 4

Concept:

• An atom consists of many orbitals which are distinguished from each other based on their shape, size, and orientation in space.
• Thus Quantum numbers are those numbers that designate and distinguish various atomic orbitals and electrons present in an atom.

There are four types of quantum number:

• Principal quantum number
  • ​Denoted by the symbol ‘n’.
  • Determines the size and to a large extent the energy of the orbital.
  • it has values n= 1,2,3,4....
• The angular quantum number determines the three-dimensional shape of the orbital quantum number.
  • Denoted by the symbol ‘l’ is also known as orbital angular momentum or subsidiary quantum number.
  • It defines the three-dimensional shape of the orbital.
  • It has values 0 to n-1.
  • The orbitals we get are l = 0 for s, l = 1 for p , l = 2 for d, l = 3 for f etc.
• Magnetic orbital quantum number
  • ​Denoted by the symbol ‘ml’.
  • Gives information about the spatial orientation of the orbital concerning a standard set of co-ordinate axis.
  • The number of ml' values gives us the number of orbitals for a particular subshell.
  • It has values - l to + l including zero.
  • A 'p' subshell has possible magnetic quantum numbers -1, 0, +1, and three orbitals are possible for p.
  • A 'd' subshell has possible magnetic quantum numbers -2, -1, 0, +1, +2 and has 5 possible orientations.
  • A 'f' subshell has  possible magnetic quantum numbers -3, -2, -1, 0, +1, +2, +3 and seven orbitals are possible for 'f'.
• Electron Spin quantum number
  • ​Denoted by the symbol (ms) refers to the orientation of the spin of the electron.
  • It has values = 1/2, - 1/2 denoting an upward and a downward spin.

Explanation:

• An electron with quantum number n = 4 and m = 2, will have quantum numbers:

Quantum Numbers	Values
Principal quantum number 'n'	4
Azimuthal quantum number 'l'.	0, 1, 2, and 3
Magnetic Quantum number 'ml'	+3, +2, +1. 0, -1, -2, -3
Spin Quantum number 's'	+1/2,  -1/2

• Thus the electrons may have the quantum number s = +1/2, and l = 0, 1, 2, and 3 but not l = 4.
• Hence, the false statement is the electrons may have the quantum number l = 4.

• The orbital given here is 4f because 7 'm' values are possible only of 'f' orbitals.