Question

# What quantum numbers specify these subshells: 1s\ 4p\ 5d\cdots\ n=?\ l=?

Equation, expression, and inequalitie
What quantum numbers specify these subshells: $$1s\ 4p\ 5d\cdots\ n=?\ l=?$$

2021-05-02
Step 1
The principal quantum number (n) for 1s is 1 and the azimuthal quantum number (l) for 1s is 0.
Calculate the range of azimuthal quantum number (l) as follows:
$$l=n-1$$
Substitute 1 for n in the above equation for the calculation of l as follows:
$$l=1-1$$
$$=0$$
The value of n is 1 and l is 0 for the 1s orbital.
The principal quantum number (n) defines the shell of the orbital. For 1s, the shell is 1.
The azimuthal quantum number (l) defines the subshell of the orbital. It is calculated as the difference between the n and 1. For 1s, the subshell is 0.
Step 2
The principal quantum number (n) for 4p is 4. Calculate the range of azimuthal quantum number (l) as follows:
$$l=n-1$$
Substitute 4 for n in the above equation for the calculation of l as follows:
$$l=4-1$$
$$=3$$
The value of l for 4p lies between 0, 1, 2, 3 . For p orbital, the value of l is 1. Therefore, the azimuthal quantum number (l) for 4p is 1.
The value of n is 4 and l is 1 for the 4p orbital.
The principal quantum number (n) defines the shell of the orbital. For 4p, the shell is 4. The azimuthal quantum number (l) defines the subshell of the orbital. It is calculated as the difference between the n and 1. For 4p orbital, the value of l can be 0, 1, 2, 3. The orbital is p. For p orbital, the azimuthal quantum number is 1. Therefore, for 4p orbital, l is 1.
Step 3
The principal quantum number (n) for 5d is 5. Calculate the range of azimuthal quantum number (l) as follows:
$$l=n-1$$
Substitute 5 for n in the above equation for the calculation of l as follows:
$$l=5-1$$
$$=4$$
The value of l for 5d lies between 0,1,2,3,4. For d orbital, the value of l is 2. Therefore, the azimuthal quantum number (l) for 5d is 2.
The value of n is 5 and l is 2 for the 5d orbital.
The principal quantum number (n) defines the shell of the orbital. For 5d, the shell is 5.
The azimuthal quantum number (l) defines the subshell of the orbital. It is calculated as the difference between the n and 1.
For 5d orbital, the value of l can be 0, 1, 2, 3, 4. The orbital is d. For d orbital, the azimuthal quantum number is 2. Therefore, for 5d orbital, l is 2.