Total Number of Orbitals with Modulus of m
Orbitals in an atom are regions in space where electrons are likely to be found. The number of orbitals with a modulus of m can be calculated using the formula 2l + 1, where l is the azimuthal quantum number.

Explanation:
- For a given value of m, there are 2l + 1 orbitals.
- The azimuthal quantum number, l, ranges from 0 to n-1, where n is the principal quantum number.
- Therefore, the total number of orbitals with modulus of m can be found by summing 2l + 1 for all possible values of l.

Example:
- Let's consider the case of n = 3 (l = 0, 1, 2) and m = 1.
- For l = 0, there is 1 orbital (2*0 + 1 = 1).
- For l = 1, there are 3 orbitals (2*1 + 1 = 3).
- For l = 2, there are 5 orbitals (2*2 + 1 = 5).
- Therefore, the total number of orbitals with modulus of m = 1 is 1 + 3 + 5 = 9.

Conclusion:
- The total number of orbitals with a modulus of m can be calculated by summing 2l + 1 for all possible values of l.
- Understanding the relationship between the azimuthal quantum number and the number of orbitals is essential in quantum mechanics and the study of atomic structure.