The electrons identified by quantum numbers n and l :
(a) n = 4, l = 1
(b) n = 4, l = 0
(c) n = 3, l = 2
(d) n = 3, l = 1
can be placed in order of increasing energy as :

Question

The electrons identified by quantum numbers n and l : 
(a) n = 4, l = 1 
(b) n = 4, l = 0 
(c) n = 3, l = 2 
(d) n = 3, l = 1 
can be placed in order of increasing energy as :

Accepted Answer

To understand why Option 3 is the correct answer, we need to consider the order of increasing energy for electrons based on their quantum numbers, specifically the principal quantum number (n) and the azimuthal quantum number (l). The energy of an electron in an atom is primarily determined by these quantum numbers, and the general rule for energy levels is that they increase with increasing values of n and l.

1. **Explanation of Option 3: (d) < (b) < (c) < (a)**
   - **(d) n = 3, l = 1**: This electron is in the 3p subshell. For n = 3, the p subshell (l = 1) is lower in energy compared to the d subshell (l = 2).
   - **(b) n = 4, l = 0**: This electron is in the 4s subshell. The 4s subshell is typically lower in energy than the 3d subshell due to electron shielding and penetration effects.
   - **(c) n = 3, l = 2**: This electron is in the 3d subshell. The 3d subshell is higher in energy than the 4s subshell because of its higher azimuthal quantum number.
   - **(a) n = 4, l = 1**: This electron is in the 4p subshell. The 4p subshell is higher in energy than the 3d subshell because it belongs to a higher principal quantum number (n = 4).

2. **Why Other Options Are Incorrect:**
   - **Option 1: (a) < (c) < (b) < (d)**
     - This option incorrectly places the 4p subshell (a) as having lower energy than the 3d subshell (c), which contradicts the typical energy order where 4p is higher than 3d.
   - **Option 2: (c) < (d) < (b) < (a)**
     - This option incorrectly places the 3d subshell (c) as having lower energy than the 3p subshell (d), which is not consistent with the energy order where 3p is lower than 3d.
   - **Option 4: (b) < (d) < (a) < (c)**
     - This option incorrectly places the 4s subshell (b) as having lower energy than the 3p subshell (d), which is not accurate since 3p is lower in energy than 4s.

In conclusion, Option 3 correctly orders the electrons by increasing energy based on their quantum numbers, adhering to the principles of electron configuration and energy levels in atoms.