4. Place the following orbitals in order of increasing energy:

1s, 3s, 4s, 6s, 3d, 4f, 3p, 7s, 5d, 5p

Using the Aufbau's principle, we can sort these orbitals into the right energy levels based on the sequence provided.

Aufbau's principle states that sublevels with lower energies are filled up before those with higher energy levels. The sublevels are not filled up based on numerical order. The sequence is given below:

1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f e. t. c

The arrangement above is based on increasing strength of the energy levels.

now we apply this to our problem to give:

1s < 3s < 3p < 4s < 3d < 5p < 6s < 4f < 5d < 7s