arrange the following subshells in order form lowest to highest energy: 4s 4p 4d 4f
To arrange the given subshells in order from lowest to highest energy, we need to understand the order of filling subshells according to the Aufbau principle and the n + l rule.
The Aufbau principle states that electrons fill the lowest energy levels and subshells first before moving to higher energy levels. According to this principle, we can see that the 4s subshell is filled before 4p, 4d, and 4f.
The n + l rule is used when two subshells have the same principal quantum number (n). In such cases, the subshell with the lower sum of the principal and azimuthal quantum numbers (n + l) is filled first. The principal quantum number (n) represents the energy level, while the azimuthal quantum number (l) represents the shape of the orbital.
Now, let's apply these principles to sort the given subshells in order from lowest to highest energy:
1. 4s: Since the 4s subshell has the lowest principal quantum number (n = 4) and azimuthal quantum number (l = 0), it is the lowest in energy.
2. 4p: The 4p subshell has the same principal quantum number (n = 4) as 4s but a higher azimuthal quantum number (l = 1). So, according to the n + l rule, it is filled after 4s.
3. 4d: The 4d subshell also has the same principal quantum number (n = 4) as 4s and 4p but has a higher azimuthal quantum number (l = 2). So, it is filled after 4s and 4p.
4. 4f: Lastly, the 4f subshell has the same principal quantum number (n = 4) as the previous subshells but the highest azimuthal quantum number (l = 3). Therefore, it is filled last among the given subshells.
Arranging the subshells in order from lowest to highest energy:
4s < 4p < 4d < 4f