To determine which of the statements (A) through (E) are correct, let's analyze each statement one by one.
### Step 1: Analyze Statement A
**Statement A:** The principal quantum number 'n' is a positive integer with values of 'n' = 1, 2, 3, ...
**Analysis:** This statement is correct. The principal quantum number (n) indeed takes positive integer values starting from 1 (n = 1, 2, 3, ...).
### Step 2: Analyze Statement B
**Statement B:** The azimuthal quantum number for a given 'n' (principal quantum number) can have values as 'l = 0, 1, 2, ... n.
**Analysis:** This statement is incorrect. The azimuthal quantum number (l) can take values from 0 to (n-1). Therefore, the correct range for l is 0 ≤ l < n.
### Step 3: Analyze Statement C
**Statement C:** The magnetic orbital quantum number 'm_l' for a particular 'l' (azimuthal quantum number) has (2l + 1) values.
**Analysis:** This statement is correct. For a given azimuthal quantum number l, the magnetic quantum number m_l can take values from -l to +l, which includes a total of (2l + 1) values.
### Step 4: Analyze Statement D
**Statement D:** `±1/2` are the two possible orientations of electron spin.
**Analysis:** This statement is correct. The spin quantum number (s) can have two possible values: +1/2 and -1/2, representing the two possible orientations of an electron's spin.
### Step 5: Analyze Statement E
**Statement E:** For l = 5, there will be a total of 9 orbitals.
**Analysis:** This statement is incorrect. For l = 5, the magnetic quantum number m_l can take values from -5 to +5, which gives a total of (2*5 + 1) = 11 orbitals, not 9.
### Conclusion
Based on the analysis:
- Statement A: Correct
- Statement B: Incorrect
- Statement C: Correct
- Statement D: Correct
- Statement E: Incorrect
Thus, the correct statements are A, C, and D.
### Final Answer
The correct statements are: A, C, and D.
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