Question

Which of the following set of quantum numbers has the highest energy?
1. n = 4, l = 0, m_l = 0
2. n = 3, l = 2, ml = -1
3. n = 3, l = 1, ml = 0
4. n = 4, l = 1, ml = -1

Answer 1

Correct Answer - Option 4 : n = 4, l = 1, ml = -1

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:

• Each set of the quantum number represents an orbital.
• The following table shows the orbital represented by each set of given quantum numbers.

 

Principal Quantum No. (n)	Magnetic Quantum No. (ml)	Azimuthal Quantum No. (l)	orbital
4	0	0	4s
3	-1	2	3d
3	0	1	3p
4	-1	1	4p

 

• The order of energy of orbitals as given by Aufbau principle is:

\(1s<2s<2p<3s<3p<4s<3d<4p<5s<4d<5p<6s<4f<5d<6p<7s<5f<6d<7p<8s\)

• Hence, the highest energy orbitals among 4s, 3d, 3p and 4p is '4p'.

Hence, n = 4, l = 1, ml = -1​ represents the highest energy.