Question

The electrons are identified 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 the order of increasing energy as
(A) (c)<(d)<(b)<(a)
(B) (d)<(b)<(c)<(a)
(C) (b)<(d)<(a)<(c)
(D) (a)<(c)<(b)<(d)

Answer 1

Hint: We can say that the configuration that has the highest (n+l) value, has the highest energy. In the configuration where the (n+l) value is the same, the configuration with lower n value is considered as low energy.

Complete step by step solution:
Here, we are given two quantum numbers of the orbitals. n stands for the principal quantum number and l stands for azimuthal quantum number.
- Principal quantum number shows the shell of the electron in the atom. So, higher the number of the shell, far it will be from the nucleus. As we go far from the nucleus, the energy of the electrons increases. So, we can say that as the number of n increases, the energy of the electrons increases.
- Azimuthal quantum numbers 1,2,3… relates to the orbitals s,p,d… etc. So, here also we can say that as the value of azimuthal quantum number increases, the energy of the electrons increases. Thus, higher the l value, higher its value will be.
- So, in order to compare the energy of the orbitals, we will do the sum of their n and l values and we can say that higher the (n+l) value, higher will be its energy. If the sum is the same, then the configuration with lower n value has lower energy.
- So, in (b) and (d) the (n+l) value is 4.
For (b), (n+l) = (4+0) = 4
For (d), (n+l) = (3+1) = 4
Here, the configuration which has low n value will have low energy. So, (d) is the configuration with least energy. Then comes (b).
- In (a) and (c), the (n+l) value if 5.
For (a), (n+l) = (4+1) = 5
For (c), (n+l) = (3+2) = 5
Here, (c) has lower n value. So, it has the lower energy in comparison with (a)
Thus, if we arrange them in increasing order of energy, then it will be (d)<(b)<(c)<(a)

So, the correct answer is (B).

Note: With this rule, we can predict the orbital configuration of the incoming electron in almost all atoms. Basically, Aufbau gave this rule stating that electrons occupy those orbitals first which have lower energy.