How many electrons in an atom can have n + l = 6 ?

The quantum numbers n and l describe the energy and shape of an electron's orbital in an atom. The sum n + l is related to the energy of the electron.

The principal quantum number n can have any positive integer value. The azimuthal quantum number l can have any integer value from 0 to n - 1.

For n + l = 6, the possible pairs (n, l) are (1, 5), (2, 4), (3, 3), (4, 2), (5, 1), and (6, 0). However, because l can only be as large as n - 1, the only valid pairs are (4, 2), (5, 1), and (6, 0).

The number of electrons in an orbital is given by 2(2l + 1). So, for each pair:

• (4, 2): 2(2*2 + 1) = 10 electrons
• (5, 1): 2(2*1 + 1) = 6 electrons
• (6, 0): 2(2*0 + 1) = 2 electrons

Adding these up, there can be a total of 10 + 6 + 2 = 18 electrons in an atom where n + l = 6.