Question

what is the lowest energy orbital in the quantum mechanical model

Answer 1

Orbital energy in the quantum mechanical model-

The energy of an orbital is to be determined through the principle quantum number (n). n =1orbital has the lowest possible energy in the atom. Higher the value of n,  higher the level of energy. For higher values of n, the level of energy becomes so high that the electron can easily escape from the atom.

The energy of an electron also depends on the interactions with the other electrons. Spatial probability distribution plays an important role in these interactions and because of the interactions, the energy levels of orbitals depend also on l (azimuthal quantum number).  Higher the values of l, higher the values of energy.

for ex, the energy level in 2p state > the energy level in 2s state

Thus, the azimuthal quantum number is relatively more important.

The energy sequence of the subshells (e.g., 1s, 2s, 2p, etc.) has shown below.

Each cell represents a subshell with n and l given by its row and column, respectively.

	s	p	d	f	g	h
1	1
2	2	3
3	4	5	7
4	6	8	10	13
5	9	11	14	17	21
6	12	15	18	22	26	31
7	16	19	23	27	32	37
8	20	24	28	33	38	44
9	25	29	34	39	45	51
10	30	35	40	46	52	59

Empty cells indicate non existing sub shells.

1s is the lowest energy orbital in the quantum mechanical model.

Energy level in descending order has shown below

1s < 2s< 2p...... and so on.