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 'mₗ' 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?

Solution

Chemistry ma’am · 3 steps

Test each statement against the rules: l stops at n − 1, and l = 5 gives 11 orbitals, not 9.

1. Statement	What the rule says	Verdict
   (A)	n = 1, 2, 3, …, any positive integer	correct
   (B)	l = 0, 1, 2, …, (n-1), so l never reaches n	wrong
   (C)	mₗ = -l, …, 0, …, +l, which is 2l + 1 values	correct
   (D)	mₛ = +1/2 or -1/2, the two spin orientations	correct
   (E)	For l = 5, orbitals = 2(5) + 1 = 11	wrong

2. Why B fails. For n = 1, statement (B) would allow l = 1, a 1p subshell, which does not exist. The largest value of l is n - 1.
3. Why E fails. Use the formula from (C). With l = 5, mₗ runs from -5 to +5, which is 11 values, so there are 11 orbitals, not 9.
4. So. The correct statements are (A), (C) and (D), which is option (c).

The idea to keep. Remember the limits: l runs from 0 to n - 1, and mₗ runs from -l to +l, giving 2l + 1 orbitals in a subshell.

Answer from the NTA final answer key. Solution by PrepWiser.