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Question 32

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 has $$(2n + 1)$$ values.
(C) Magnetic orbital quantum number 'm' for a particular 'l' (azimuthal quantum number) has $$(2l + 1)$$ values.
(D) $$\pm \frac{1}{2}$$ 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?

Let us analyze each statement.

Statement (A): "The principal quantum number 'n' is a positive integer with values of $$n = 1, 2, 3, \dots$$." This is correct. The principal quantum number is always a positive integer.

Statement (B): "The azimuthal quantum number 'l' for a given 'n' can have values as $$l = 0, 1, 2, \dots, n$$ and has $$(2n + 1)$$ values." This is incorrect because the azimuthal quantum number $$l$$ ranges from $$0$$ to $$(n - 1)$$, giving $$n$$ values, not $$(2n + 1)$$ values, and $$l$$ goes up to $$(n - 1)$$, not $$n$$.

Statement (C): "Magnetic orbital quantum number 'm' for a particular 'l' has $$(2l + 1)$$ values." This is correct. The magnetic quantum number $$m_l$$ ranges from $$-l$$ to $$+l$$, giving $$(2l + 1)$$ values.

Statement (D): "$$\pm \frac{1}{2}$$ are the two possible orientations of electron spin." This is correct. The spin quantum number $$m_s$$ can be $$+\frac{1}{2}$$ or $$-\frac{1}{2}$$.

Statement (E): "For $$l = 5$$, there will be a total of 9 orbitals." This is incorrect because for $$l = 5$$, the number of orbitals is $$(2l + 1) = 2(5) + 1 = 11$$, not $$9$$.

The correct statements are (A), (C) and (D).

Hence, the correct answer is Option C.

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