Calculation of Total Orbital Angular Momentum of np6 Electronic System

Definition of Total Orbital Angular Momentum:
Total orbital angular momentum is the sum of the angular momenta of all the electrons present in an atom.

Calculation Steps:
1. Determine the value of n for the np6 electronic configuration.
2. For each electron, determine the value of l (angular momentum quantum number).
3. Determine the value of ml (magnetic quantum number) for each electron.
4. Calculate the total angular momentum for each electron using the formula:
L = sqrt(l(l+1))h/2pi, where h/2pi is the reduced Planck constant.
5. Add up the angular momenta of all the electrons to obtain the total orbital angular momentum.

Calculation for np6 Electronic Configuration:
1. n = 5 (since the electronic configuration is np6, where n = 5 for the p subshell)
2. For each electron, l = 1 (since the p subshell has l = 1)
3. There are 6 electrons, with ml values of -1, 0, and 1 (since there are three orbitals in the p subshell)
4. Using the formula, the total angular momentum for each electron is:
L = sqrt(1(1+1))h/2pi = sqrt(2)h/2pi
5. Adding up the angular momenta of all the electrons:
Total L = 6(sqrt(2)h/2pi) = 6sqrt(2)h/2pi
Simplifying the expression, we get:
Total L = 3sqrt(2)h/pi

Final Answer:
The total orbital angular momentum of the np6 electronic system is 1 (in atomic units).