List these electron subshells in order of increasing energy

List these electron subshells in order of increasing energy.

3d
5s
4s
4p

The correct answer and explanation is :

To order the given electron subshells in terms of increasing energy, we need to consider the principal quantum number (n) and the angular momentum quantum number (l), which together determine the energy of a subshell. The general rule is that the energy increases with the increase in ( n ) and ( l ), but when subshells have the same ( n ), the one with the lower ( l ) value will generally have lower energy.

Let’s examine the given subshells:

1. 3d (n = 3, l = 2)
2. 5s (n = 5, l = 0)
3. 4s (n = 4, l = 0)
4. 4p (n = 4, l = 1)

Now, let’s break them down:

Step 1: Understanding the Energy Ordering Rule

The energy of electron subshells is generally determined by a combination of the principal quantum number ( n ) and the azimuthal quantum number ( l ). The general energy ordering follows this pattern:

• For subshells with the same ( n ), the higher the ( l ), the higher the energy.
• For subshells with different ( n ), the energy tends to increase with increasing ( n ), though there are exceptions when the ( l )-value varies significantly.

Step 2: Apply the Rule to the Given Subshells

• 3d has ( n = 3 ), ( l = 2 ). This is a ( d )-subshell, which is relatively higher in energy compared to ( s )- and ( p )-subshells with lower ( l ).
• 5s has ( n = 5 ), ( l = 0 ). Even though ( n ) is higher than 4 or 3, ( s )-subshells have the lowest energy for any given ( n ).
• 4s has ( n = 4 ), ( l = 0 ). This is a ( s )-subshell, and as a rule, ( s )-subshells have lower energy than ( p )- or ( d )-subshells with the same ( n ).
• 4p has ( n = 4 ), ( l = 1 ). The ( p )-subshell is higher in energy than the ( s )-subshell for the same ( n ).

Step 3: Order the Subshells

• 4s will have the lowest energy because it’s an ( s )-subshell with ( n = 4 ).
• 4p will have a higher energy than ( 4s ) because ( p )-subshells are higher in energy than ( s )-subshells with the same ( n ).
• 3d will have a higher energy than ( 4p ) because although it has a lower ( n ), ( d )-subshells are generally higher in energy than ( p )-subshells with the same ( n ).
• 5s will have the highest energy because ( s )-subshells with higher ( n ) have more energy than those with a lower ( n ).

Thus, the order of increasing energy is:

4s < 4p < 3d < 5s

Step 4: Visualization

Here is a diagram showing the electron subshells ordered by increasing energy. You can clearly see the subshells ordered from lowest to highest energy: 4s < 4p < 3d < 5s.