Question

Consider the following statements :
(A) The principal quantum number ‘n’ is a positive integer with values of ‘n’ = 1, 2, 3, ….
(B) The azimuthal quantum number ‘l’ for a given ‘n’ (principal quantum number) can have values as ‘l’ = 0, 1, 2, …n
(C) Magnetic orbital quantum number ‘m_l’ for a particular ‘l’ (azimuthal quantum number) has (2l + 1) values.
(D) ±1/2 are the two possible orientations of electron spin.
(E) For l = 5, there will be a total of 9 orbital
Which of the above statements are correct?

• A. (A), (B) and (C)
• B. (A), (C), (D) and (E)
• C. (A), (C) and (D)
• D. (A), (B), (C) and (D)

Answer 1

The Correct Option is C

Let's evaluate the correctness of each statement:

1. Statement A: The principal quantum number 'n' is a positive integer with values of 'n' = 1, 2, 3, …. This statement is correct. The principal quantum number 'n' defines the energy level of an electron in an atom and can take any positive integer value starting from 1.
2. Statement B: The azimuthal quantum number 'l' for a given 'n' (principal quantum number) can have values as 'l' = 0, 1, 2, …n. This statement is incorrect. The azimuthal quantum number 'l' can have values ranging from 0 to \(n-1\), not up to \(n\). So for a given 'n', the possible 'l' values are 0, 1, 2, ..., \(n-1\).
3. Statement C: Magnetic orbital quantum number 'm_l' for a particular 'l' (azimuthal quantum number) has (2l + 1) values. This statement is correct. The magnetic quantum number 'm_l' can take values from \(-l\) to \(+l\), including 0, giving a total of \(2l + 1\) possible values.
4. Statement D: ±1/2 are the two possible orientations of electron spin. This statement is correct. The electron spin quantum number, denoted by 's', can take two possible values: \(+\frac{1}{2}\) or \(-\frac{1}{2}\), representing the two possible spin orientations.
5. Statement E: For \(l = 5\), there will be a total of 9 orbitals. This statement is incorrect. For a given azimuthal quantum number 'l', the number of orbitals is equal to \(2l + 1\). Substituting \(l = 5\) gives \(2(5) + 1 = 11\) orbitals, not 9.

Based on the above analysis, the statements (A), (C), and (D) are correct. Thus, the answer is:

(A), (C) and (D)