# (n+l) rule and its applications

#### ByChemistry Fundamentals

Nov 23, 2020

(n+l) Rule

From this rule, we can get information about the difference in energy between two orbitals. According to the Aufbau principle, electrons are filled into atomic orbitals in the increasing order of orbital energy level.
(n+l) rule helps to determine which one between two given orbitals will occupy by an electron.

As we know that there are four quantum numbers, namely, principal(n), azimuthal(l), magnetic(m), and spin(s) quantum numbers. They are used to describe the position and energy of the electron in an atom.

Relation between n and l:

1. n can have values of 1,2,3,4……..(only integers)
2. for a given n value, l can have values starting from 0 to (n-1), i.e a total of n values.
3. for the values of l equal to 0, 1, 2, 3, the subshell notations are s, p, d, and f, respectively.

when n = 1, l should have one value and it is 0.

Similarly, n =2, values of l are 0, 1.

(n + l) value for different orbitals

1. For 3d orbitals: n = 3 and l = 2. Therefore, value of (n+l) = (3+2) = 5
2. Similarly, for 4s orbitals: n = 4, and l = 0. So, value of (n+l) = (4+0) = 4

** From the above calculation, we can say that the energy of 3d orbital is greater than that of 4s orbital. According to the Aufbau principle, the last electron will enter the 4s orbital rather than the 3d orbital.

Q: The 19th electron in the K atom enters into the 4s orbital instead of 3d orbital-Explain?

Hints: See the above discussion.

Q: Which one will occupy first by electron between 3d and 4p orbitals?

Ans: (n+l) value for 3d orbital is 5 [ because n = 3 and l =2] and this value for 4p orbital is also 5 [ here n = 4 and l = 1].

For both cases, the value of (n+l) is the same. In this situation, the orbital with a higher principal quantum number (n) have greater energy than that of the remaining orbital. Therefore, the energy of 4p> 3d. For this reason, the electron will enter into the 3d orbital rather than the 4p orbital.

Q: The 37th electron of Rb enters into the 5s orbital instead of 4d orbital-Explain.

Ans: We can explain this by the help of (n+l) rule.

For 4d orbital, value of (n+l) = (4 +2) = 6 ( here n =4 and l = 2)

Value of (n+l) for 5s orbital = (5+O) = 5 (( here n =5and l = 0)

Therefore, the energy of 5s orbital is lower than that of 4d orbital. According to the Aufbau principle, the 37th electron of Rb will enter into the 5s orbital instead of 4d orbital.

IMPORTANT NOTE: Please memorize the following chart to solve the above problems successfully.