Consider the following sets of quantum numbers (n, l) for an electron in an atom: (A) n=1, l=0 (B) n=2, l=2 (C) n=3, l=1 (D) n=3, l=3 How many of the given sets of quantum numbers are physically possible?

Step-by-step solution

For a given principal quantum number n , the allowed values for the azimuthal quantum number l are integers from 0 to (n-1) . Let us evaluate each given set: (A) n=1, l=0 : This is possible and represents the 1s orbital. (B) n=2, l=2 : This is not possible because the maximum value of l for n=2 is n-1 = 1 . (C) n=3, l=1 : This is possible and represents the 3p orbital. (D) n=3, l=3 : This is not possible because the maximum value of l for n=3 is n-1 = 2 . Thus, only two sets, (A) and (C), are physically possible. A