It is true that the set of three quantum numbers n, l, and ml together specify a particular orbital. So it may be confusing to you that there are some orbitals for which the value of ml is not identified. If you review your notes, you will find, for example:A 1s orbital corresponds to n = 1, l = 0, and ml = 0.A 2pz orbital corresponds to n = 2, l = 1, and ml = 0.We can also say that the 2px and 2py orbitals both correspond to n = 2, l = 1, BUT we cannot identify a value of ml for each; the two values ml = 1 and -1 belong to both orbitals together but there is no one-to-one correspondence. (The technical reason for this is that orbitals are not simply functions in real space but rather in "complex space", if you know what complex numbers are (they contain imaginary components, i = √-1). For purposes of portraying the orbitals in real space, we transform the complex functions into real functions by taking linear combinations.)A 3s orbital corresponds to n = Answer 1 Question 10, l = Answer 2 Question 10, ml = Answer 3 Question 10.A 3px orbital corresponds to n = Answer 4 Question 10, l = Answer 5 Question 10, ml = Answer 6 Question 10.A 3dx2-y2 orbital corresponds to n = Answer 7 Question 10, l = Answer 8 Question 10, ml = Answer 9 Question 10.
Question
It is true that the set of three quantum numbers n, l, and ml together specify a particular orbital. So it may be confusing to you that there are some orbitals for which the value of ml is not identified. If you review your notes, you will find, for example:A 1s orbital corresponds to n = 1, l = 0, and ml = 0.A 2pz orbital corresponds to n = 2, l = 1, and ml = 0.We can also say that the 2px and 2py orbitals both correspond to n = 2, l = 1, BUT we cannot identify a value of ml for each; the two values ml = 1 and -1 belong to both orbitals together but there is no one-to-one correspondence. (The technical reason for this is that orbitals are not simply functions in real space but rather in "complex space", if you know what complex numbers are (they contain imaginary components, i = √-1). For purposes of portraying the orbitals in real space, we transform the complex functions into real functions by taking linear combinations.)A 3s orbital corresponds to n = Answer 1 Question 10, l = Answer 2 Question 10, ml = Answer 3 Question 10.A 3px orbital corresponds to n = Answer 4 Question 10, l = Answer 5 Question 10, ml = Answer 6 Question 10.A 3dx2-y2 orbital corresponds to n = Answer 7 Question 10, l = Answer 8 Question 10, ml = Answer 9 Question 10.
Solution
The quantum numbers for the given orbitals are as follows:
A 3s orbital corresponds to n = 3, l = 0, and ml = 0.
A 3px orbital corresponds to n = 3, l = 1, and ml = -1 or 1 (it's not possible to specify which one, as explained above).
A 3dx2-y2 orbital corresponds to n = 3, l = 2, and ml = 2 or -2 (again, it's not possible to specify which one).
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