Question

Which of the following represents the correct set of the four quantum numbers for 4d electron?
1. 4, 3, 3, +1/2
2. 4, 2, 1, 0
3. 4, 3, -2, +1/2
4. 4, 2, 1, -1/2

Answer 1

Correct Answer - Option 4 : 4, 2, 1, -1/2

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.
• 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:

• The four quantum numbers are represented as 'n' , 'l', 'm_l', 's'.
• In the set of quantum numbers 4, 3, 3, +1/2, the azimuthal quantum number is 3, which is for an 'f' orbital. Hence the set of quantum numbers does not represent an electron in 4d orbital.
• In the set of quantum numbers 4, 2, 1, 0, the spin given is 0. The only possible values of spin quantum numbers are  +1/2, - 1/2, so the set of quantum numbers is not correct.
• In the set of quantum numbers 4, 3, -2, +1/2, n = 4, l = 3, 'l' is not of a d orbital, hence it is not the correct representation of 4d orbital.
• In the set of quantum numbers 4, 2, 1, -1/2, n = 4, l = 2, m_l = 1, s = -1/2, l = 2 is for d orbital. Hence, this set represents electrons in a 4d orbital.

Hence, 4, 2, 1, -1/2  represents the correct set of the four quantum numbers for 4d electron​.